#pragma GCC target("avx512f,bmi")
#include <immintrin.h>
#include <stdint.h>
#include <algorithm>
#include <cassert>
#include <iostream>

using u32 = uint32_t;
using u64 = uint64_t;
#define inline __inline__ __attribute__((always_inline))
namespace simd {
    using i512 = __m512i;
    using u32x16 = u32 __attribute__((vector_size(64)));
    using u64x8 = u64 __attribute__((vector_size(64)));

    inline u32x16 load_u32x16(u32 *ptr) {
        return (u32x16)(_mm512_load_si512((i512 *)ptr));
    }
    inline u32x16 loadu_u32x16(u32 *ptr) {
        return (u32x16)(_mm512_loadu_si512((i512 *)ptr));
    }
    inline void store_u32x16(u32 *ptr, u32x16 val) {
        _mm512_store_si512((i512 *)ptr, (i512)(val));
    }
    inline void storeu_u32x16(u32 *ptr, u32x16 val) {
        _mm512_storeu_si512((i512 *)ptr, (i512)(val));
    }

    inline u32x16 set1_u32x16(u32 val) {
        return (u32x16)(_mm512_set1_epi32(val));
    }
    inline u64x8 set1_u64x8(u64 val) {
        return (u64x8)(_mm512_set1_epi64(val));
    }

    inline u32x16 setr_u32x16_si256(u32 a0, u32 a1, u32 a2, u32 a3, u32 a4, u32 a5, u32 a6, u32 a7) {
        return (u32x16)_mm512_broadcast_i64x4(_mm256_setr_epi32(a0, a1, a2, a3, a4, a5, a6, a7));
    }
    inline u64x8 setr_u64x8_si256(u64 a0, u64 a1, u64 a2, u64 a3) {
        return (u64x8)_mm512_broadcast_i64x4(_mm256_setr_epi64x(a0, a1, a2, a3));
    }

    inline u64x8 setr_u64x8(u64 a0, u64 a1, u64 a2, u64 a3, u64 a4, u64 a5, u64 a6, u64 a7) {
        return (u64x8)_mm512_setr_epi64(a0, a1, a2, a3, a4, a5, a6, a7);
    }

    template <int imm8>
    inline u32x16 shuffle_u32x16(u32x16 val) {
        return (u32x16)(_mm512_shuffle_epi32((i512)(val), (_MM_PERM_ENUM)imm8));
    }
    constexpr inline u32x16 permute_u32x16(u32x16 val, u32x16 p) {
        return (u32x16)(_mm512_permutexvar_epi32((i512)(p), (i512)(val)));
    }

    template <int imm8>
    constexpr inline u32x16 permute_u32x16_epi128(u32x16 a) {
        return (u32x16)(_mm512_shuffle_i64x2((i512)(a), (i512)(a), imm8));
    }

    template <int imm16>
    constexpr inline u32x16 blend_u32x16(u32x16 a, u32x16 b) {
        return (u32x16)(_mm512_mask_blend_epi32(imm16, (i512)(a), (i512)(b)));
    }
    template <int imm8>
    constexpr inline u32x16 blend_u32x16_si256(u32x16 a, u32x16 b) {
        return (u32x16)(_mm512_mask_blend_epi32(imm8 | (imm8 << 8), (i512)(a), (i512)(b)));
    }

    constexpr inline u32x16 shift_right_u32x16_epi64(u32x16 val, int imm8) {
        return (u32x16)(_mm512_srli_epi64((i512)(val), imm8));
    }

    constexpr inline u32x16 min_u32x16(u32x16 a, u32x16 b) {
        return (u32x16)(_mm512_min_epu32((i512)(a), (i512)(b)));
    }
    constexpr inline u32x16 mul64_u32x16(u32x16 a, u32x16 b) {
        return (u32x16)(_mm512_mul_epu32((i512)(a), (i512)(b)));
    }

};  // namespace simd
using namespace simd;

struct Montgomery {
    u32 mod;
    u32 mod2;   // 2 * mod
    u32 n_inv;  // n_inv * mod == -1 (mod 2^32)
    u32 r;      // 2^32 % mod
    u32 r2;     // (2^32) ^ 2 % mod

    constexpr Montgomery() = default;
    constexpr Montgomery(u32 mod) : mod(mod) {
        assert(mod % 2);
        assert(mod < (1 << 30));
        n_inv = 1;
        for (int i = 0; i < 5; i++) {
            n_inv *= 2u + n_inv * mod;
        }
        assert(n_inv * mod == -1u);

        mod2 = 2 * mod;
        r = (1ULL << 32) % mod;
        r2 = r * u64(r) % mod;
    }

    constexpr inline u32 shrink(u32 val) const {
        return std::min(val, val - mod);
    }
    constexpr inline u32 shrink2(u32 val) const {
        return std::min(val, val - mod2);
    }
    constexpr inline u32 shrink2_n(u32 val) const {
        return std::min(val, val + mod2);
    }

    template <bool strict = false>
    constexpr inline u32 mul(u32 a, u32 b) const {
        u64 val = u64(a) * b;
        u32 res = (val + u32(val) * n_inv * u64(mod)) >> 32;
        if constexpr (strict)
            res = shrink(res);
        return res;
    }
};

// Montgomery32
struct Montgomery_simd {
    alignas(64) u32x16 mod, mod2, n_inv, r, r2;

    constexpr inline Montgomery_simd() = default;
    constexpr inline Montgomery_simd(u32 md) {
        Montgomery mt(md);
        mod = set1_u32x16(mt.mod);
        mod2 = set1_u32x16(mt.mod2);
        n_inv = set1_u32x16(mt.n_inv);
        r = set1_u32x16(mt.r);
        r2 = set1_u32x16(mt.r2);
    }

    constexpr inline u32x16 shrink(u32x16 val) const {
        return min_u32x16(val, val - mod);
    }
    constexpr inline u32x16 shrink2(u32x16 val) const {
        return min_u32x16(val, val - mod2);
    }
    constexpr inline u32x16 shrink2_n(u32x16 val) const {
        return min_u32x16(val, val + mod2);
    }

    template <bool strict = false>
    constexpr inline u32x16 mul(u32x16 a, u32x16 b) const {
        u32x16 x0246 = mul64_u32x16(a, b);
        u32x16 x1357 = mul64_u32x16(shift_right_u32x16_epi64(a, 32), shift_right_u32x16_epi64(b, 32));
        u32x16 x0246_ninv = mul64_u32x16(x0246, n_inv);
        u32x16 x1357_ninv = mul64_u32x16(x1357, n_inv);
        u32x16 res = blend_u32x16_si256<0b10101010>(shift_right_u32x16_epi64(u32x16((u64x8)x0246 + (u64x8)mul64_u32x16(x0246_ninv, mod)), 32),
                                                       u32x16((u64x8)x1357 + (u64x8)mul64_u32x16(x1357_ninv, mod)));
        if constexpr (strict) res = shrink(res);
        return res;
    }

    template <bool strict = false>
    constexpr inline u64x8 mul_to_hi(u64x8 a, u64x8 b) const {
        u32x16 val = mul64_u32x16((u32x16)a, (u32x16)b);
        u32x16 val_ninv = mul64_u32x16(val, n_inv);
        u32x16 res = u32x16(u64x8(val) + u64x8(mul64_u32x16(val_ninv, mod)));
        if constexpr (strict)
            res = shrink(res);
        return (u64x8)res;
    }

    template <bool strict = false>
    constexpr inline u64x8 mul(u64x8 a, u64x8 b) const {
        return (u64x8)shift_right_u32x16_epi64((u32x16)mul_to_hi<strict>(a, b), 32);
    }
};
#include <array>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <vector>

struct FFT {
    alignas(64) Montgomery_simd mts;
    Montgomery mt;
    u32 mod, g;

    constexpr inline u32 power(u32 base, u32 exp) const {
        const auto mt = this->mt;
        u32 res = mt.r;
        for (; exp > 0; exp >>= 1) {
            if (exp & 1) res = mt.mul(res, base);
            base = mt.mul(base, base);
        }
        return mt.shrink(res);
    }

    constexpr inline u32 find_pr_root(u32 mod) const {
        u32 m = mod - 1;
        std::vector<u32> vec;
        for (u32 i = 2; u64(i) * i <= m; i++) if (m % i == 0) {
            vec.push_back(i);
            do m /= i; while (m % i == 0);
        }
        if (m != 1) vec.push_back(m);
        for (u32 i = 2;; i++) if (std::all_of(vec.begin(), vec.end(), [&](u32 f) { return mt.r != power(mt.mul(i, mt.r2), (mod - 1) / f); }))
            return i;
    }

    static constexpr u32 LG = 30;
    alignas(64) u32 w[8], w_r[8];

    alignas(64) u64x8 w_cum_x8[LG], w_rcum_x8[LG];     // read FFT()
    alignas(64) u32x16 w_cum_x16[LG], w_rcum_x16[LG];  // read FFT()

    constexpr inline FFT(u32 mod = 998'244'353) : mt(mod), mts(mod), mod(mod) {
        const auto mt = this->mt;

        g = mt.mul<true>(mt.r2, find_pr_root(mod));

        for (u32 i = 0; i ^ LG; i++) {
            u32 f = power(g, u64(mod - 1) >> i + 3);
            u32 res = mt.mul<true>(f, power(power(f, (1 << i + 1) - 2), mod - 2)), res_r = power(res, mod - 2);
            w_cum_x8[i] = setr_u64x8_si256(res, power(res, 2), res, power(res, 3));
            w_rcum_x8[i] = setr_u64x8_si256(res_r, power(res_r, 2), res_r, power(res_r, 3));
        }
        for (u32 i = 0; i ^ LG; i++) {
            u32 f = power(g, u64(mod - 1) >> i + 5);
            f = mt.mul<true>(f, power(power(f, (1 << i + 1) - 2), mod - 2));
            u32 f1 = f, f2 = mt.mul<true>(f1, f1), f4 = mt.mul<true>(f2, f2), f8 = mt.mul<true>(f4, f4);
            w_cum_x16[i] = (u32x16)setr_u32x16_si256(f1, f2, f1, f4, f1, f2, f1, f8);

            u32 f_r = power(f, mod - 2);
            w_rcum_x16[i][0] = mt.r;
            for (u32 j = 1; j ^ 16; j++) w_rcum_x16[i][j] = mt.mul<true>(w_rcum_x16[i][j - 1], f_r);
        }

        w[0] = mt.r;
        w_r[0] = mt.r;
        for (int k = 0; k < 3; k++) {
            u32 f = power(g, (mod - 1) >> k + 2);
            u32 f_r = power(f, mod - 2);

            for (int j = 0; j < (1 << k); j++)
                w[(1 << k) + j] = mt.mul<true>(w[j], f), w_r[(1 << k) + j] = mt.mul<true>(w_r[j], f_r);
        }
    }

    constexpr inline void fft(u32 lg, u32 *data) const {
        const auto mt = this->mt;    // ! to put Montgomery constants in registers
        const auto mts = this->mts;  // ! to put Montgomery constants in registers

        int n = 1 << lg;
        int k = lg;

        if (lg % 2 == 1) {
            for (int i = 0; i < n / 2; i += 16) {
                u32x16 a = load_u32x16(data + i);
                u32x16 b = load_u32x16(data + n / 2 + i);

                store_u32x16(data + i, mts.shrink2(a + b));
                store_u32x16(data + n / 2 + i, mts.shrink2_n(a - b));
            }
            k--;
        }

        assert(k % 2 == 0);
        for (; k > 4; k -= 2) {
            u64x8 wj_cum = set1_u64x8(mt.r);
            u32x16 w_1 = set1_u32x16(w[1]);
            for (int i = 0; i < n; i += (1 << k)) {
                u32x16 w1 = shuffle_u32x16<0b00'00'00'00>((u32x16)wj_cum);
                u32x16 w2 = permute_u32x16((u32x16)wj_cum, set1_u32x16(2));
                u32x16 w3 = permute_u32x16((u32x16)wj_cum, set1_u32x16(6));
                wj_cum = mts.mul<true>(wj_cum, w_cum_x8[__builtin_ctz(~(i >> k))]);

                for (int j = 0; j < (1 << k - 2); j += 16) {
                    u32x16 a = load_u32x16(data + i + 0 * (1 << k - 2) + j);
                    u32x16 b = load_u32x16(data + i + 1 * (1 << k - 2) + j);
                    u32x16 c = load_u32x16(data + i + 2 * (1 << k - 2) + j);
                    u32x16 d = load_u32x16(data + i + 3 * (1 << k - 2) + j);

                    a = mts.shrink2(a);
                    b = mts.mul(b, w1), c = mts.mul(c, w2), d = mts.mul(d, w3);

                    u32x16 a1 = mts.shrink2(a + c), b1 = mts.shrink2(b + d),
                           c1 = mts.shrink2_n(a - c), d1 = mts.mul(b + mts.mod2 - d, w_1);

                    store_u32x16(data + i + 0 * (1 << k - 2) + j, a1 + b1);
                    store_u32x16(data + i + 1 * (1 << k - 2) + j, a1 + mts.mod2 - b1);
                    store_u32x16(data + i + 2 * (1 << k - 2) + j, c1 + d1);
                    store_u32x16(data + i + 3 * (1 << k - 2) + j, c1 + mts.mod2 - d1);
                }
            }
        }

        assert(k == 4);
        u32x16 cum = (u32x16)_mm512_setr_epi32(w[0], w[0], w[1], w[0],   // [ w         | w^2       | w * w_1    | w^4       ]
                                               w[2], w[1], w[3], w[0],   // [ w * w_2   | w^2 * w_1 | w * w_3    | w^8       ]
                                               w[4], w[2], w[5], w[1],   // [ w * w_4   | w^2 * w_2 | w * w_5    | w^4 * w_1 ]
                                               w[6], w[3], w[7], w[0]);  // [ w * w_6   | w^2 * w_3 | w * w_7    | w^8       ]
        int n_16 = n / 16;
        for (int i = 0; i < n_16; i++) {
            u32x16 val = load_u32x16(data + i * 16);

            u64x8 w3 = (u64x8)cum;  // no shuffle needed
            u64x8 w2 = (u64x8)shuffle_u32x16<0b00'01'00'01>(cum);
            u64x8 w1 = (u64x8)permute_u32x16(cum, (u32x16)setr_u64x8(3, 3, 3, 3, 11, 11, 11, 11));
            u64x8 w0 = (u64x8)permute_u32x16(cum, (u32x16)setr_u64x8(7, 7, 7, 7, 15, 15, 15, 15));
            cum = mts.mul<true>(cum, w_cum_x16[__builtin_ctz(~i)]);

            u32x16 bw;

            val = mts.shrink2(val);
            bw = permute_u32x16((u32x16)mts.mul_to_hi(w0, (u64x8)permute_u32x16(val, (u32x16)setr_u64x8(8, 9, 10, 11, 12, 13, 14, 15))),
                                (u32x16)setr_u32x16_si256(1, 3, 5, 7, 9, 11, 13, 15));
            val = permute_u32x16_epi128<0b01'00'01'00>(val) + blend_u32x16<0xFF00>(bw, mts.mod2 - bw);

            val = mts.shrink2(val);
            bw = permute_u32x16((u32x16)mts.mul_to_hi(w1, (u64x8)permute_u32x16(val, (u32x16)setr_u64x8(4, 5, 6, 7, 12, 13, 14, 15))),
                                (u32x16)_mm512_setr_epi32(1, 3, 5, 7, 1, 3, 5, 7,
                                                          9, 11, 13, 15, 9, 11, 13, 15));
            val = permute_u32x16_epi128<0b10'10'00'00>(val) + blend_u32x16<0xF0F0>(bw, mts.mod2 - bw);

            val = mts.shrink2(val);
            bw = shuffle_u32x16<0b11'01'11'01>((u32x16)mts.mul_to_hi(w2, (u64x8)shuffle_u32x16<0b00'11'00'10>(val)));
            val = shuffle_u32x16<0b01'00'01'00>(val) + blend_u32x16_si256<0b11'00'11'00>(bw, mts.mod2 - bw);

            val = mts.shrink2(val);
            bw = shuffle_u32x16<0b11'11'01'01>((u32x16)mts.mul_to_hi(w3, (u64x8)shuffle_u32x16<0b00'11'00'01>(val)));
            val = shuffle_u32x16<0b10'10'00'00>(val) + blend_u32x16_si256<0b10'10'10'10>(bw, mts.mod2 - bw);

            store_u32x16(data + i * 16, val);
        }
    }

    constexpr inline void ifft(int lg, u32 *data, u32 fc = -1u) const {
        const auto mt = this->mt;
        const auto mts = this->mts;

        if (fc == -1u) {
            fc = mt.r;
        }

        int n = 1 << lg;
        int k = 1;

        u32x16 cum2 = (u32x16)_mm512_setr_epi32(w_r[0], w_r[0], w_r[0], w_r[1], w_r[0], w_r[2], w_r[0], w_r[3],
                                                w_r[0], w_r[4], w_r[0], w_r[5], w_r[0], w_r[6], w_r[0], w_r[7]);
        u32x16 cum1 = (u32x16)_mm512_setr_epi32(w_r[0], w_r[0], w_r[0], w_r[0], w_r[0], w_r[0], w_r[1], w_r[1],
                                                w_r[0], w_r[0], w_r[2], w_r[2], w_r[0], w_r[0], w_r[3], w_r[3]);
        u32x16 cum0 = (u32x16)_mm512_setr_epi32(w_r[0], w_r[0], w_r[0], w_r[0], w_r[0], w_r[0], w_r[0], w_r[0],
                                                w_r[0], w_r[0], w_r[0], w_r[0], w_r[1], w_r[1], w_r[1], w_r[1]);
        const u32 inv_2 = mt.mul<true>(mt.r2, (mod + 1) / 2);
        u32x16 cum = set1_u32x16(mt.mul<true>(fc, power(inv_2, lg)));

        int n_16 = n / 16;
        for (int i = 0; i < n_16; i++) {
            u32x16 vec = load_u32x16(data + i * 16);

            vec = mts.mul(cum2, blend_u32x16_si256<0b10'10'10'10>(vec, mts.mod2 - vec) + shuffle_u32x16<0b10'11'00'01>(vec));
            vec = mts.mul(cum1, blend_u32x16_si256<0b11'00'11'00>(vec, mts.mod2 - vec) + shuffle_u32x16<0b01'00'11'10>(vec));
            vec = mts.mul(cum0, blend_u32x16<0xF0F0>(vec, mts.mod2 - vec) + permute_u32x16_epi128<0b10'11'00'01>(vec));
            vec = mts.mul(cum, blend_u32x16<0xFF00>(vec, mts.mod2 - vec) + permute_u32x16_epi128<0b01'00'11'10>(vec));

            store_u32x16(data + i * 16, vec);

            cum = mts.mul<true>(cum, w_rcum_x16[__builtin_ctz(~i)]);
        }
        k += 4;

        assert(k == 5);

        for (; k + 1 <= lg; k += 2) {
            u64x8 wj_cum = set1_u64x8(mt.r);
            u32x16 w_1 = set1_u32x16(w_r[1]);

            for (int i = 0; i < n; i += (1 << k + 1)) {
                u32x16 w1 = shuffle_u32x16<0b00'00'00'00>((u32x16)wj_cum);
                u32x16 w2 = permute_u32x16((u32x16)wj_cum, set1_u32x16(2));
                u32x16 w3 = permute_u32x16((u32x16)wj_cum, set1_u32x16(6));
                wj_cum = mts.mul<true>(wj_cum, w_rcum_x8[__builtin_ctz(~(i >> k + 1))]);

                for (int j = 0; j < (1 << k - 1); j += 16) {
                    u32x16 a = load_u32x16(data + i + 0 * (1 << k - 1) + j);
                    u32x16 b = load_u32x16(data + i + 1 * (1 << k - 1) + j);
                    u32x16 c = load_u32x16(data + i + 2 * (1 << k - 1) + j);
                    u32x16 d = load_u32x16(data + i + 3 * (1 << k - 1) + j);

                    u32x16 a1 = mts.shrink2(a + b), b1 = mts.shrink2_n(a - b),
                           c1 = mts.shrink2(c + d), d1 = mts.mul(c + mts.mod2 - d, w_1);

                    store_u32x16(data + i + 0 * (1 << k - 1) + j, mts.shrink2(a1 + c1));
                    store_u32x16(data + i + 1 * (1 << k - 1) + j, mts.mul(w1, b1 + d1));
                    store_u32x16(data + i + 2 * (1 << k - 1) + j, mts.mul(w2, a1 + mts.mod2 - c1));
                    store_u32x16(data + i + 3 * (1 << k - 1) + j, mts.mul(w3, b1 + mts.mod2 - d1));
                }
            }
        }
        if (k == lg) {
            for (int i = 0; i < n / 2; i += 16) {
                u32x16 a = load_u32x16(data + i);
                u32x16 b = load_u32x16(data + n / 2 + i);

                store_u32x16(data + i, mts.shrink(mts.shrink2(a + b)));
                store_u32x16(data + n / 2 + i, mts.shrink(mts.shrink2_n(a - b)));
            }
        } else {
            assert(k == lg + 1);
            for (int i = 0; i < n; i += 16) {
                u32x16 ai = load_u32x16(data + i);
                store_u32x16(data + i, mts.shrink(ai));
            }
        }
    }

    constexpr inline void convolve(int lg, __restrict__ u32 *a, __restrict__ u32 *b) const {
        if (lg <= 4) {
            int n = (1 << lg);
            __restrict__ u32 *c = (u32 *)_mm_malloc(n * 4, 4);
            memset(c, 0, 4 * n);
            for (u32 i = 0; i < n; i++) for (u32 j = 0; j < n; j++)
                c[(i + j) & (n - 1)] = mt.shrink2(c[(i + j) & (n - 1)] + mt.mul(a[i], b[j]));
            for (int i = 0; i < n; i++) a[i] = mt.mul<true>(mt.r2, c[i]);
            _mm_free(c);
            return;
        }

        fft(lg, a);
        fft(lg, b);

        const auto mts = this->mts;  // ! to put Montgomery constants in registers
        for (int i = 0; i < (1 << lg); i += 16) {
            u32x16 ai = load_u32x16(a + i), bi = load_u32x16(b + i);
            store_u32x16(a + i, mts.mul(mts.shrink2(ai), mts.shrink2(bi)));
        }

        ifft(lg, a, mt.r2);
    }

    constexpr inline std::vector<u32> convolve(const std::vector<u32> &a, const std::vector<u32> &b) const {
        int sz = std::max(0, (int)a.size() + (int)b.size() - 1);

        int lg = std::__lg(std::max(1, sz - 1)) + 1;
        u32 *ap = (u32 *)_mm_malloc(std::max(64, (1 << lg) * 4), 64);
        u32 *bp = (u32 *)_mm_malloc(std::max(64, (1 << lg) * 4), 64);
        memset(ap, 0, 4 << lg);
        memset(bp, 0, 4 << lg);

        std::copy(a.begin(), a.end(), ap);
        std::copy(b.begin(), b.end(), bp);

        convolve(lg, ap, bp);

        std::vector<u32> res(ap, ap + sz);
        _mm_free(ap);
        _mm_free(bp);
        return res;
    }
};
#include <sys/mman.h>
#include <sys/stat.h>

#include <algorithm>
#include <cstring>
#include <iostream>

using u32 = uint32_t;
using u64 = uint64_t;

namespace QIO_base {
    constexpr int O_buffer_default_size = 1 << 18;
    constexpr int O_buffer_default_flush_threshold = 40;
    struct _int_to_char_tab {
        char tab[40000];
        constexpr inline _int_to_char_tab() : tab() {
            for (int i = 0; i != 10000; ++i) {
                for (int j = 3, n = i; ~j; --j) {
                    tab[i * 4 + j] = n % 10 + 48, n /= 10;
                }
            }
        }
    } constexpr _otab;
}  // namespace QIO_base
namespace QIO_I {
    using namespace QIO_base;
    struct Qinf {
        FILE *f;
        char *bg, *ed, *p;
        struct stat Fl;
        constexpr inline Qinf(FILE *fi) : f(fi) {
            int fd = fileno(f);
            fstat(fd, &Fl);
            bg = (char *)mmap(0, Fl.st_size + 1, PROT_READ, MAP_PRIVATE, fd, 0);
            p = bg, ed = bg + Fl.st_size;
            madvise(p, Fl.st_size + 1, MADV_SEQUENTIAL);
        }
        constexpr inline ~Qinf() { munmap(bg, Fl.st_size + 1); }
        constexpr inline void skip_space() {
            while (*p <= ' ') ++p;
        }
        char get() { return *p++; }
        char seek() { return *p; }
        bool eof() { return p == ed; }
        Qinf &read(char *s, size_t count) { return memcpy(s, p, count), p += count, *this; }
        Qinf &operator>>(u32 &x) {
            skip_space(), x = 0;
            for (; *p > ' '; ++p) {
                x = x * 10 + (*p & 0xf);
            }
            return *this;
        }
        Qinf &operator>>(int &x) {
            skip_space();
            if (*p == '-') {
                for (++p, x = 48 - *p++; *p > ' '; ++p) {
                    x = x * 10 - (*p ^ 48);
                }
            } else {
                for (x = *p++ ^ 48; *p > ' '; ++p) {
                    x = x * 10 + (*p ^ 48);
                }
            }
            return *this;
        }
    } qin(stdin);
}  // namespace QIO_I
namespace QIO_O {
    using namespace QIO_base;
    struct Qoutf {
        FILE *f;
        char *bg, *ed, *p;
        char *ed_thre;
        int fp;
        u64 _fpi;
        Qoutf(FILE *fo, size_t sz = O_buffer_default_size) : f(fo), bg(new char[sz]), ed(bg + sz), p(bg), ed_thre(ed - O_buffer_default_flush_threshold), fp(6), _fpi(1000000ull) {}
        void flush() { fwrite_unlocked(bg, 1, p - bg, f), p = bg; }
        void chk() {
            if (__builtin_expect(p > ed_thre, 0)) flush();
        }
        ~Qoutf() {
            flush();
            delete[] bg;
        }
        void put4(u32 x) {
            if (x > 99u) {
                if (x > 999u) {
                    memcpy(p, _otab.tab + (x << 2) + 0, 4), p += 4;
                } else {
                    memcpy(p, _otab.tab + (x << 2) + 1, 3), p += 3;
                }
            } else {
                if (x > 9u) {
                    memcpy(p, _otab.tab + (x << 2) + 2, 2), p += 2;
                } else {
                    *p++ = x ^ 48;
                }
            }
        }
        void put2(u32 x) {
            if (x > 9u) memcpy(p, _otab.tab + (x << 2) + 2, 2), p += 2;
            else *p++ = x ^ 48;
        }
        Qoutf &write(const char *s, size_t count) {
            if (count > 1024 || p + count > ed_thre) {
                flush(), fwrite_unlocked(s, 1, count, f);
            } else {
                memcpy(p, s, count), p += count, chk();
            }
            return *this;
        }
        Qoutf &operator<<(char ch) { return *p++ = ch, *this; }
        Qoutf &operator<<(u32 x) {
            if (x > 9999u) {
                put4(x / 10000u);
                memcpy(p, _otab.tab + ((x % 10000u) << 2), 4), p += 4;
            } else {
                put4(x);
            }
            return chk(), *this;
        }
    } qout(stdout);
}  // namespace QIO_O
namespace QIO {
    using QIO_I::qin;
    using QIO_I::Qinf;
    using QIO_O::qout;
    using QIO_O::Qoutf;
}  // namespace QIO
using namespace QIO;
#include <cassert>
#include <iostream>

int32_t main() {
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(nullptr), std::cout.tie(nullptr);

    FFT fft(998'244'353);

    int n, m;
    qin >> n >> m;
    ++n, ++m;

    int lg = std::__lg(std::max(1, n + m - 2)) + 1;

    u32 *a = (u32 *)_mm_malloc(std::max(64, (1 << lg) * 4), 64),
        *b = (u32 *)_mm_malloc(std::max(64, (1 << lg) * 4), 64);

    for (u32 i = 0; i < n; i++) qin >> a[i];
    memset(a + n, 0, (4 << lg) - 4 * n);
    for (u32 i = 0; i < m; i++) qin >> b[i];
    memset(b + m, 0, (4 << lg) - 4 * m);
    fft.convolve(lg, a, b);

    for (u32 i = 0; i < (n + m - 1); i++)
        qout << a[i] << " \n"[i + 1 == (n + m - 1)];
}

answer.code: In function ‘constexpr simd::u32x16 simd::permute_u32x16(simd::u32x16, simd::u32x16)’:
answer.code:52:49: error: call to non-‘constexpr’ function ‘__m512i _mm512_permutexvar_epi32(__m512i, __m512i)’
   52 |         return (u32x16)(_mm512_permutexvar_epi32((i512)(p), (i512)(val)));
      |                        ~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
In file included from /usr/lib/gcc/x86_64-linux-gnu/11/include/immintrin.h:49,
                 from answer.code:2:
/usr/lib/gcc/x86_64-linux-gnu/11/include/avx512fintrin.h:6947:1: note: ‘__m512i _mm512_permutexvar_epi32(__m512i, __m512i)’ declared here
 6947 | _mm512_permutexvar_epi32 (__m512i __X, __m512i __Y)
      | ^~~~~~~~~~~~~~~~~~~~~~~~
answer.code: In function ‘constexpr simd::u32x16 simd::shift_right_u32x16_epi64(simd::u32x16, int)’:
answer.code:70:42: error: call to non-‘constexpr’ function ‘__m512i _mm512_srli_epi64(__m512i, unsigned int)’
   70 |         return (u32x16)(_mm512_srli_epi64((i512)(val), imm8));
      |                        ~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~
In file included from /usr/lib/gcc/x86_64-linux-gnu/11/include/immintrin.h:49,
                 from answer.code:2:
/usr/lib/gcc/x86_64-linux-gnu/11/include/avx512fintrin.h:1082:1: note: ‘__m512i _mm512_srli_epi64(__m512i, unsigned int)’ declared here
 1082 | _mm512_srli_epi64 (__m512i __A, unsigned int __B)
      | ^~~~~~~~~~~~~~~~~
answer.code: In function ‘constexpr simd::u32x16 simd::min_u32x16(simd::u32x16, simd::u32x16)’:
answer.code:74:41: error: call to non-‘constexpr’ function ‘__m512i _mm512_min_epu32(__m512i, __m512i)’
   74 |         return (u32x16)(_mm512_min_epu32((i512)(a), (i512)(b)));
      |                        ~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~
In file included from /usr/lib/gcc/x86_64-linux-gnu/11/include/immintrin.h:49,
                 from answer.code:2:
/usr/lib/gcc/x86_64-linux-gnu/11/include/avx512fintrin.h:11430:1: note: ‘__m512i _mm512_min_epu32(__m512i, __m512i)’ declared here
11430 | _mm512_min_epu32 (__m512i __A, __m512i __B)
      | ^~~~~~~~~~~~~~~~
answer.code: In function ‘constexpr simd::u32x16 simd::mul64_u32x16(simd::u32x16, simd::u32x16)’:
answer.code:77:41: error: call to non-‘constexpr’ function ‘__m512i _mm512_mul_epu32(__m512i, __m512i)’
   77 |         return (u32x16)(_mm512_mul_epu32((i512)(a), (i512)(b)));
      |                        ~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~
In file included from /usr/lib/gcc/x86_64-linux-gnu/11/include/immintrin.h:49,
                 from answer.code:2:
/usr/lib/gcc/x86_64-linux-gnu/11/include/avx512fintrin.h:971:1: note: ‘__m512i _mm512_mul_epu32(__m512i, __m512i)’ declared here
  971 | _mm512_mul_epu32 (__m512i __X, __m512i __Y)
      | ^~~~~~~~~~~~~~~~
answer.code: In member function ‘constexpr u32 FFT::find_pr_root(u32) const’:
answer.code:199:26: error: variable ‘vec’ of non-literal type ‘std::vector<unsigned int>’ in ‘constexpr’ function
  199 |         std::vector<u32> vec;
      |                          ^~~
In file included from /usr/include/c++/11/vector:67,
                 from /usr/include/c++/11/functional:62,
                 from /usr/include/c++/11/pstl/glue_algorithm_defs.h:13,
                 from /usr/include/c++/11/algorithm:74,
                 from answer.code:4:
/usr/include/c++/11/bits/stl_vector.h:389:11: note: ‘std::vector<unsigned int>’ is not literal because:
  389 |     class vector : protected _Vector_base<_Tp, _Alloc>
      |           ^~~~~~
/usr/include/c++/11/bits/stl_vector.h:389:11: note:   ‘std::vector<unsigned int>’ does not have ‘constexpr’ destructor
In file included from /usr/lib/gcc/x86_64-linux-gnu/11/include/immintrin.h:49,
                 from answer.code:2:
answer.code: In member function ‘constexpr void FFT::fft(u32, u32*) const’:
answer.code:297:30: error: call to non-‘constexpr’ function ‘__m512i _mm512_set_epi32(int, int, int, int, int, int, int, int, int, int, int, int, int, int, int, int)’
  297 |         u32x16 cum = (u32x16)_mm512_setr_epi32(w[0], w[0], w[1], w[0],   // [ w         | w^2       | w * w_1    | w^4       ]
      |                              ^~~~~~~~~~~~~~~~~
/usr/lib/gcc/x86_64-linux-gnu/11/include/avx512fintrin.h:90:1: note: ‘__m512i _mm512_set_epi32(int, int, int, int, int, int, int, int, int, int, int, int, int, int, int, int)’ declared here
   90 | _mm512_set_epi32 (int __A, int __B, int __C, int __D,
      | ^~~~~~~~~~~~~~~~
answer.code: In member function ‘constexpr void FFT::ifft(int, u32*, u32) const’:
answer.code:347:31: error: call to non-‘constexpr’ function ‘__m512i _mm512_set_epi32(int, int, int, int, int, int, int, int, int, int, int, int, int, int, int, int)’
  347 |         u32x16 cum2 = (u32x16)_mm512_setr_epi32(w_r[0], w_r[0], w_r[0], w_r[1], w_r[0], w_r[2], w_r[0], w_r[3],
      |                               ^~~~~~~~~~~~~~~~~
/usr/lib/gcc/x86_64-linux-gnu/11/include/avx512fintrin.h:90:1: note: ‘__m512i _mm512_set_epi32(int, int, int, int, int, int, int, int, int, int, ...