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ID题目提交者结果用时内存语言文件大小提交时间测评时间
#807198#1816. Multiple ParenthesesZi_GaoAC ✓544ms102408kbC++2319.1kb2024-12-09 19:57:452024-12-09 19:57:45

Judging History

你现在查看的是最新测评结果

  • [2024-12-09 19:57:45]
  • 评测
  • 测评结果:AC
  • 用时:544ms
  • 内存:102408kb
  • [2024-12-09 19:57:45]
  • 提交

answer

#include<bits/stdc++.h>
// #define ONLINE_JUDGE
#define INPUT_DATA_TYPE int
#define OUTPUT_DATA_TYPE int
inline __attribute((always_inline)) INPUT_DATA_TYPE read(){register INPUT_DATA_TYPE x=0;register char f=0,c=getchar();while(c<'0'||'9'<c)f=(c=='-'),c=getchar();while('0'<=c&&c<='9')x=(x<<3)+(x<<1)+(c&15),c=getchar();return f?-x:x;}void print(OUTPUT_DATA_TYPE x){if(x<0)x=-x,putchar('-');if(x>9)print(x/10);putchar(x%10^48);return;}

using namespace std;
template <typename mint>
struct FormalPowerSeries : vector<mint> {
	using vector<mint>::vector;
	using FPS = FormalPowerSeries;

	FPS &operator+=(const FPS &r) {
		if (r.size() > this->size()) this->resize(r.size());
		for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];
		return *this;
	}

	FPS &operator+=(const mint &r) {
		if (this->empty()) this->resize(1);
		(*this)[0] += r;
		return *this;
	}

	FPS &operator-=(const FPS &r) {
		if (r.size() > this->size()) this->resize(r.size());
		for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];
		return *this;
	}

	FPS &operator-=(const mint &r) {
		if (this->empty()) this->resize(1);
		(*this)[0] -= r;
		return *this;
	}

	FPS &operator*=(const mint &v) {
		for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v;
		return *this;
	}

	FPS &operator/=(const FPS &r) {
		if (this->size() < r.size()) {
			this->clear();
			return *this;
		}
		int n = this->size() - r.size() + 1;
		if ((int)r.size() <= 64) {
			FPS f(*this), g(r);
			g.shrink();
			mint coeff = g.back().inverse();
			for (auto &x : g) x *= coeff;
			int deg = (int)f.size() - (int)g.size() + 1;
			int gs = g.size();
			FPS quo(deg);
			for (int i = deg - 1; i >= 0; i--) {
				quo[i] = f[i + gs - 1];
				for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j];
			}
			*this = quo * coeff;
			this->resize(n, mint(0));
			return *this;
		}
		return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();
	}

	FPS &operator%=(const FPS &r) {
		*this -= *this / r * r;
		shrink();
		return *this;
	}

	FPS operator+(const FPS &r) const { return FPS(*this) += r; }
	FPS operator+(const mint &v) const { return FPS(*this) += v; }
	FPS operator-(const FPS &r) const { return FPS(*this) -= r; }
	FPS operator-(const mint &v) const { return FPS(*this) -= v; }
	FPS operator*(const FPS &r) const { return FPS(*this) *= r; }
	FPS operator*(const mint &v) const { return FPS(*this) *= v; }
	FPS operator/(const FPS &r) const { return FPS(*this) /= r; }
	FPS operator%(const FPS &r) const { return FPS(*this) %= r; }
	FPS operator-() const {
		FPS ret(this->size());
		for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i];
		return ret;
	}

	void shrink() {
		while (this->size() && this->back() == mint(0)) this->pop_back();
	}

	FPS rev() const {
		FPS ret(*this);
		reverse(begin(ret), end(ret));
		return ret;
	}

	FPS dot(FPS r) const {
		FPS ret(min(this->size(), r.size()));
		for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i];
		return ret;
	}

	// 前 sz 項を取ってくる。sz に足りない項は 0 埋めする
	FPS pre(int sz) const {
		FPS ret(begin(*this), begin(*this) + min((int)this->size(), sz));
		if ((int)ret.size() < sz) ret.resize(sz);
		return ret;
	}

	FPS operator>>(int sz) const {
		if ((int)this->size() <= sz) return {};
		FPS ret(*this);
		ret.erase(ret.begin(), ret.begin() + sz);
		return ret;
	}

	FPS operator<<(int sz) const {
		FPS ret(*this);
		ret.insert(ret.begin(), sz, mint(0));
		return ret;
	}

	FPS diff() const {
		const int n = (int)this->size();
		FPS ret(max(0, n - 1));
		mint one(1), coeff(1);
		for (int i = 1; i < n; i++) {
			ret[i - 1] = (*this)[i] * coeff;
			coeff += one;
		}
		return ret;
	}

	FPS integral() const {
		const int n = (int)this->size();
		FPS ret(n + 1);
		ret[0] = mint(0);
		if (n > 0) ret[1] = mint(1);
		auto mod = mint::get_mod();
		for (int i = 2; i <= n; i++) ret[i] = (-ret[mod % i]) * (mod / i);
		for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i];
		return ret;
	}

	mint eval(mint x) const {
		mint r = 0, w = 1;
		for (auto &v : *this) r += w * v, w *= x;
		return r;
	}

	FPS log(int deg = -1) const {
		assert(!(*this).empty() && (*this)[0] == mint(1));
		if (deg == -1) deg = (int)this->size();
		return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
	}

	FPS pow(int64_t k, int deg = -1) const {
		const int n = (int)this->size();
		if (deg == -1) deg = n;
		if (k == 0) {
			FPS ret(deg);
			if (deg) ret[0] = 1;
			return ret;
		}
		for (int i = 0; i < n; i++) {
			if ((*this)[i] != mint(0)) {
				mint rev = mint(1) / (*this)[i];
				FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg);
				ret *= (*this)[i].pow(k);
				ret = (ret << (i * k)).pre(deg);
				if ((int)ret.size() < deg) ret.resize(deg, mint(0));
				return ret;
			}
			if (__int128_t(i + 1) * k >= deg) return FPS(deg, mint(0));
		}
		return FPS(deg, mint(0));
	}

	static void *ntt_ptr;
	static void set_fft();
	FPS &operator*=(const FPS &r);
	void ntt();
	void intt();
	void ntt_doubling();
	static int ntt_pr();
	FPS inv(int deg = -1) const;
	FPS exp(int deg = -1) const;
};
template <typename mint>
void *FormalPowerSeries<mint>::ntt_ptr = nullptr;


template <typename mint>
struct NTT {
  static constexpr uint32_t get_pr() {
    uint32_t _mod = mint::get_mod();
    using u64 = uint64_t;
    u64 ds[32] = {};
    int idx = 0;
    u64 m = _mod - 1;
    for (u64 i = 2; i * i <= m; ++i) {
      if (m % i == 0) {
        ds[idx++] = i;
        while (m % i == 0) m /= i;
      }
    }
    if (m != 1) ds[idx++] = m;

    uint32_t _pr = 2;
    while (1) {
      int flg = 1;
      for (int i = 0; i < idx; ++i) {
        u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;
        while (b) {
          if (b & 1) r = r * a % _mod;
          a = a * a % _mod;
          b >>= 1;
        }
        if (r == 1) {
          flg = 0;
          break;
        }
      }
      if (flg == 1) break;
      ++_pr;
    }
    return _pr;
  };

  static constexpr uint32_t mod = mint::get_mod();
  static constexpr uint32_t pr = get_pr();
  static constexpr int level = __builtin_ctzll(mod - 1);
  mint dw[level], dy[level];

  void setwy(int k) {
    mint w[level], y[level];
    w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
    y[k - 1] = w[k - 1].inverse();
    for (int i = k - 2; i > 0; --i)
      w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
    dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
    for (int i = 3; i < k; ++i) {
      dw[i] = dw[i - 1] * y[i - 2] * w[i];
      dy[i] = dy[i - 1] * w[i - 2] * y[i];
    }
  }

  NTT() { setwy(level); }

  void fft4(vector<mint> &a, int k) {
    if ((int)a.size() <= 1) return;
    if (k == 1) {
      mint a1 = a[1];
      a[1] = a[0] - a[1];
      a[0] = a[0] + a1;
      return;
    }
    if (k & 1) {
      int v = 1 << (k - 1);
      for (int j = 0; j < v; ++j) {
        mint ajv = a[j + v];
        a[j + v] = a[j] - ajv;
        a[j] += ajv;
      }
    }
    int u = 1 << (2 + (k & 1));
    int v = 1 << (k - 2 - (k & 1));
    mint one = mint(1);
    mint imag = dw[1];
    while (v) {
      // jh = 0
      {
        int j0 = 0;
        int j1 = v;
        int j2 = j1 + v;
        int j3 = j2 + v;
        for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
          mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
          mint t0p2 = t0 + t2, t1p3 = t1 + t3;
          mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
          a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;
          a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;
        }
      }
      // jh >= 1
      mint ww = one, xx = one * dw[2], wx = one;
      for (int jh = 4; jh < u;) {
        ww = xx * xx, wx = ww * xx;
        int j0 = jh * v;
        int je = j0 + v;
        int j2 = je + v;
        for (; j0 < je; ++j0, ++j2) {
          mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,
               t3 = a[j2 + v] * wx;
          mint t0p2 = t0 + t2, t1p3 = t1 + t3;
          mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
          a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;
          a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;
        }
        xx *= dw[__builtin_ctzll((jh += 4))];
      }
      u <<= 2;
      v >>= 2;
    }
  }

  void ifft4(vector<mint> &a, int k) {
    if ((int)a.size() <= 1) return;
    if (k == 1) {
      mint a1 = a[1];
      a[1] = a[0] - a[1];
      a[0] = a[0] + a1;
      return;
    }
    int u = 1 << (k - 2);
    int v = 1;
    mint one = mint(1);
    mint imag = dy[1];
    while (u) {
      // jh = 0
      {
        int j0 = 0;
        int j1 = v;
        int j2 = v + v;
        int j3 = j2 + v;
        for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
          mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
          mint t0p1 = t0 + t1, t2p3 = t2 + t3;
          mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;
          a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;
          a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;
        }
      }
      // jh >= 1
      mint ww = one, xx = one * dy[2], yy = one;
      u <<= 2;
      for (int jh = 4; jh < u;) {
        ww = xx * xx, yy = xx * imag;
        int j0 = jh * v;
        int je = j0 + v;
        int j2 = je + v;
        for (; j0 < je; ++j0, ++j2) {
          mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];
          mint t0p1 = t0 + t1, t2p3 = t2 + t3;
          mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
          a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;
          a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;
        }
        xx *= dy[__builtin_ctzll(jh += 4)];
      }
      u >>= 4;
      v <<= 2;
    }
    if (k & 1) {
      u = 1 << (k - 1);
      for (int j = 0; j < u; ++j) {
        mint ajv = a[j] - a[j + u];
        a[j] += a[j + u];
        a[j + u] = ajv;
      }
    }
  }

  void ntt(vector<mint> &a) {
    if ((int)a.size() <= 1) return;
    fft4(a, __builtin_ctz(a.size()));
  }

  void intt(vector<mint> &a) {
    if ((int)a.size() <= 1) return;
    ifft4(a, __builtin_ctz(a.size()));
    mint iv = mint(a.size()).inverse();
    for (auto &x : a) x *= iv;
  }

  vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
    int l = a.size() + b.size() - 1;
    if (min<int>(a.size(), b.size()) <= 40) {
      vector<mint> s(l);
      for (int i = 0; i < (int)a.size(); ++i)
        for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];
      return s;
    }
    int k = 2, M = 4;
    while (M < l) M <<= 1, ++k;
    setwy(k);
    vector<mint> s(M);
    for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];
    fft4(s, k);
    if (a.size() == b.size() && a == b) {
      for (int i = 0; i < M; ++i) s[i] *= s[i];
    } else {
      vector<mint> t(M);
      for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];
      fft4(t, k);
      for (int i = 0; i < M; ++i) s[i] *= t[i];
    }
    ifft4(s, k);
    s.resize(l);
    mint invm = mint(M).inverse();
    for (int i = 0; i < l; ++i) s[i] *= invm;
    return s;
  }

  void ntt_doubling(vector<mint> &a) {
    int M = (int)a.size();
    auto b = a;
    intt(b);
    mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
    for (int i = 0; i < M; i++) b[i] *= r, r *= zeta;
    ntt(b);
    copy(begin(b), end(b), back_inserter(a));
  }
};



template <typename mint>
void FormalPowerSeries<mint>::set_fft() {
  if (!ntt_ptr) ntt_ptr = new NTT<mint>;
}

template <typename mint>
FormalPowerSeries<mint>& FormalPowerSeries<mint>::operator*=(
    const FormalPowerSeries<mint>& r) {
  if (this->empty() || r.empty()) {
    this->clear();
    return *this;
  }
  set_fft();
  auto ret = static_cast<NTT<mint>*>(ntt_ptr)->multiply(*this, r);
  return *this = FormalPowerSeries<mint>(ret.begin(), ret.end());
}

template <typename mint>
void FormalPowerSeries<mint>::ntt() {
  set_fft();
  static_cast<NTT<mint>*>(ntt_ptr)->ntt(*this);
}

template <typename mint>
void FormalPowerSeries<mint>::intt() {
  set_fft();
  static_cast<NTT<mint>*>(ntt_ptr)->intt(*this);
}

template <typename mint>
void FormalPowerSeries<mint>::ntt_doubling() {
  set_fft();
  static_cast<NTT<mint>*>(ntt_ptr)->ntt_doubling(*this);
}

template <typename mint>
int FormalPowerSeries<mint>::ntt_pr() {
  set_fft();
  return static_cast<NTT<mint>*>(ntt_ptr)->pr;
}

template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {
  assert((*this)[0] != mint(0));
  if (deg == -1) deg = (int)this->size();
  FormalPowerSeries<mint> res(deg);
  res[0] = {mint(1) / (*this)[0]};
  for (int d = 1; d < deg; d <<= 1) {
    FormalPowerSeries<mint> f(2 * d), g(2 * d);
    for (int j = 0; j < min((int)this->size(), 2 * d); j++) f[j] = (*this)[j];
    for (int j = 0; j < d; j++) g[j] = res[j];
    f.ntt();
    g.ntt();
    for (int j = 0; j < 2 * d; j++) f[j] *= g[j];
    f.intt();
    for (int j = 0; j < d; j++) f[j] = 0;
    f.ntt();
    for (int j = 0; j < 2 * d; j++) f[j] *= g[j];
    f.intt();
    for (int j = d; j < min(2 * d, deg); j++) res[j] = -f[j];
  }
  return res.pre(deg);
}

template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {
  using fps = FormalPowerSeries<mint>;
  assert((*this).size() == 0 || (*this)[0] == mint(0));
  if (deg == -1) deg = this->size();

  fps inv;
  inv.reserve(deg + 1);
  inv.push_back(mint(0));
  inv.push_back(mint(1));

  auto inplace_integral = [&](fps& F) -> void {
    const int n = (int)F.size();
    auto mod = mint::get_mod();
    while ((int)inv.size() <= n) {
      int i = inv.size();
      inv.push_back((-inv[mod % i]) * (mod / i));
    }
    F.insert(begin(F), mint(0));
    for (int i = 1; i <= n; i++) F[i] *= inv[i];
  };

  auto inplace_diff = [](fps& F) -> void {
    if (F.empty()) return;
    F.erase(begin(F));
    mint coeff = 1, one = 1;
    for (int i = 0; i < (int)F.size(); i++) {
      F[i] *= coeff;
      coeff += one;
    }
  };

  fps b{1, 1 < (int)this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};
  for (int m = 2; m < deg; m *= 2) {
    auto y = b;
    y.resize(2 * m);
    y.ntt();
    z1 = z2;
    fps z(m);
    for (int i = 0; i < m; ++i) z[i] = y[i] * z1[i];
    z.intt();
    fill(begin(z), begin(z) + m / 2, mint(0));
    z.ntt();
    for (int i = 0; i < m; ++i) z[i] *= -z1[i];
    z.intt();
    c.insert(end(c), begin(z) + m / 2, end(z));
    z2 = c;
    z2.resize(2 * m);
    z2.ntt();
    fps x(begin(*this), begin(*this) + min<int>(this->size(), m));
    x.resize(m);
    inplace_diff(x);
    x.push_back(mint(0));
    x.ntt();
    for (int i = 0; i < m; ++i) x[i] *= y[i];
    x.intt();
    x -= b.diff();
    x.resize(2 * m);
    for (int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = mint(0);
    x.ntt();
    for (int i = 0; i < 2 * m; ++i) x[i] *= z2[i];
    x.intt();
    x.pop_back();
    inplace_integral(x);
    for (int i = m; i < min<int>(this->size(), 2 * m); ++i) x[i] += (*this)[i];
    fill(begin(x), begin(x) + m, mint(0));
    x.ntt();
    for (int i = 0; i < 2 * m; ++i) x[i] *= y[i];
    x.intt();
    b.insert(end(b), begin(x) + m, end(x));
  }
  return fps{begin(b), begin(b) + deg};
}


template <uint32_t mod>
struct LazyMontgomeryModInt {
	using mint = LazyMontgomeryModInt;
	using i32 = int32_t;
	using u32 = uint32_t;
	using u64 = uint64_t;

	static constexpr u32 get_r() {
		u32 ret = mod;
		for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
		return ret;
	}

	static constexpr u32 r = get_r();
	static constexpr u32 n2 = -u64(mod) % mod;
	static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
	static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
	static_assert(r * mod == 1, "this code has bugs.");

	u32 a;

	constexpr LazyMontgomeryModInt() : a(0) {}
	constexpr LazyMontgomeryModInt(const int64_t &b)
			: a(reduce(u64(b % mod + mod) * n2)){};

	static constexpr u32 reduce(const u64 &b) {
		return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
	}

	constexpr mint &operator+=(const mint &b) {
		if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
		return *this;
	}

	constexpr mint &operator-=(const mint &b) {
		if (i32(a -= b.a) < 0) a += 2 * mod;
		return *this;
	}

	constexpr mint &operator*=(const mint &b) {
		a = reduce(u64(a) * b.a);
		return *this;
	}

	constexpr mint &operator/=(const mint &b) {
		*this *= b.inverse();
		return *this;
	}

	constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
	constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
	constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
	constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
	constexpr bool operator==(const mint &b) const {
		return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
	}
	constexpr bool operator!=(const mint &b) const {
		return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
	}
	constexpr mint operator-() const { return mint() - mint(*this); }
	constexpr mint operator+() const { return mint(*this); }

	constexpr mint pow(u64 n) const {
		mint ret(1), mul(*this);
		while (n > 0) {
			if (n & 1) ret *= mul;
			mul *= mul;
			n >>= 1;
		}
		return ret;
	}

	constexpr mint inverse() const {
		int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
		while (y > 0) {
			t = x / y;
			x -= t * y, u -= t * v;
			tmp = x, x = y, y = tmp;
			tmp = u, u = v, v = tmp;
		}
		return mint{u};
	}

	// friend ostream &operator<<(ostream &os, const mint &b) {
	// 	return os << b.get();
	// }

	// friend istream &operator>>(istream &is, mint &b) {
	// 	int64_t t;
	// 	is >> t;
	// 	b = LazyMontgomeryModInt<mod>(t);
	// 	return (is);
	// }

	constexpr u32 get() const {
		u32 ret = reduce(a);
		return ret >= mod ? ret - mod : ret;
	}

	static constexpr u32 get_mod() { return mod; }
};

const long long mod=998244353;
using mint=LazyMontgomeryModInt<998244353>;
using Poly=FormalPowerSeries<mint>;

#define PC_DATA_TYPE long long

const PC_DATA_TYPE PC_MOD=mod;
const PC_DATA_TYPE PC_DATA_SIZE=2000010;

PC_DATA_TYPE inv[PC_DATA_SIZE],fact[PC_DATA_SIZE],invfact[PC_DATA_SIZE];

void init_pc(int n){
    register int i;
    for(inv[0]=0,inv[1]=fact[0]=fact[1]=invfact[0]=invfact[1]=1,i=2;i<=n;++i)
        invfact[i]=invfact[i-1]*(inv[i]=PC_MOD-PC_MOD/i*inv[PC_MOD%i]%PC_MOD)%PC_MOD,fact[i]=fact[i-1]*i%PC_MOD;
    return;
}

PC_DATA_TYPE A(int n,int m){
    if(n<0||m<0||n<m) return 0;
    return fact[n]*invfact[n-m]%PC_MOD;
}
PC_DATA_TYPE C(int n,int m){
    if(n<0||m<0||n<m) return 0;
    return fact[n]*invfact[n-m]%PC_MOD*invfact[m]%PC_MOD;
}

int main(){
	#ifndef ONLINE_JUDGE
	freopen("name.in", "r", stdin);
	freopen("name.out", "w", stdout);
	#endif

	Poly A;
    register int i;
    int n=read();
    int m=read();
    int k=read();

    init_pc(m*2);

    for(i=0;i<=m;++i)
        A.push_back(i==k?0:(C(i*2,i)*inv[i+1]%mod));

	A=(A.log()*n).exp();
	print(A[m].get());

	#ifndef ONLINE_JUDGE
	fclose(stdin);
	fclose(stdout);
	#endif
	return 0;
}

詳細信息

Test #1:

score: 100
Accepted
time: 1ms
memory: 7736kb

input:

2 2 1

output:

4

result:

ok answer is '4'

Test #2:

score: 0
Accepted
time: 1ms
memory: 7728kb

input:

1 1 1

output:

0

result:

ok answer is '0'

Test #3:

score: 0
Accepted
time: 0ms
memory: 7756kb

input:

24 120 30

output:

379268651

result:

ok answer is '379268651'

Test #4:

score: 0
Accepted
time: 2ms
memory: 8072kb

input:

1451 1598 1130

output:

884873572

result:

ok answer is '884873572'

Test #5:

score: 0
Accepted
time: 1ms
memory: 8092kb

input:

1324 1742 1033

output:

856733047

result:

ok answer is '856733047'

Test #6:

score: 0
Accepted
time: 1ms
memory: 7840kb

input:

1378 1614 1335

output:

869903701

result:

ok answer is '869903701'

Test #7:

score: 0
Accepted
time: 0ms
memory: 7876kb

input:

1071 1907 1281

output:

327700529

result:

ok answer is '327700529'

Test #8:

score: 0
Accepted
time: 0ms
memory: 7892kb

input:

1204 1337 1277

output:

475981175

result:

ok answer is '475981175'

Test #9:

score: 0
Accepted
time: 1ms
memory: 7952kb

input:

146 246 100

output:

404402509

result:

ok answer is '404402509'

Test #10:

score: 0
Accepted
time: 1ms
memory: 7956kb

input:

226 183 144

output:

351921989

result:

ok answer is '351921989'

Test #11:

score: 0
Accepted
time: 1ms
memory: 7804kb

input:

234 287 158

output:

658959115

result:

ok answer is '658959115'

Test #12:

score: 0
Accepted
time: 0ms
memory: 7760kb

input:

242 156 122

output:

325586111

result:

ok answer is '325586111'

Test #13:

score: 0
Accepted
time: 0ms
memory: 7756kb

input:

168 271 135

output:

181613866

result:

ok answer is '181613866'

Test #14:

score: 0
Accepted
time: 1ms
memory: 7740kb

input:

22 25 1

output:

684860973

result:

ok answer is '684860973'

Test #15:

score: 0
Accepted
time: 1ms
memory: 7944kb

input:

45 22 15

output:

217501624

result:

ok answer is '217501624'

Test #16:

score: 0
Accepted
time: 0ms
memory: 7940kb

input:

47 29 16

output:

690840771

result:

ok answer is '690840771'

Test #17:

score: 0
Accepted
time: 1ms
memory: 7684kb

input:

2 25 25

output:

660660974

result:

ok answer is '660660974'

Test #18:

score: 0
Accepted
time: 1ms
memory: 7772kb

input:

32 34 11

output:

133387056

result:

ok answer is '133387056'

Test #19:

score: 0
Accepted
time: 61ms
memory: 17560kb

input:

88196 118335 104471

output:

7192211

result:

ok answer is '7192211'

Test #20:

score: 0
Accepted
time: 25ms
memory: 13300kb

input:

142215 57117 51272

output:

627598793

result:

ok answer is '627598793'

Test #21:

score: 0
Accepted
time: 26ms
memory: 13332kb

input:

102255 60360 51525

output:

447649003

result:

ok answer is '447649003'

Test #22:

score: 0
Accepted
time: 59ms
memory: 18320kb

input:

132449 83413 54230

output:

215816803

result:

ok answer is '215816803'

Test #23:

score: 0
Accepted
time: 60ms
memory: 18420kb

input:

68499 95762 77190

output:

393029560

result:

ok answer is '393029560'

Test #24:

score: 0
Accepted
time: 529ms
memory: 91592kb

input:

751951 751951 1

output:

804170883

result:

ok answer is '804170883'

Test #25:

score: 0
Accepted
time: 0ms
memory: 7820kb

input:

804420 1962 410

output:

869056555

result:

ok answer is '869056555'

Test #26:

score: 0
Accepted
time: 26ms
memory: 15604kb

input:

828607 63739 13

output:

926542030

result:

ok answer is '926542030'

Test #27:

score: 0
Accepted
time: 10ms
memory: 9004kb

input:

472167 20529 23

output:

142703540

result:

ok answer is '142703540'

Test #28:

score: 0
Accepted
time: 251ms
memory: 46420kb

input:

363438 363438 1

output:

764563597

result:

ok answer is '764563597'

Test #29:

score: 0
Accepted
time: 544ms
memory: 101024kb

input:

1000000 1000000 628333

output:

283487375

result:

ok answer is '283487375'

Test #30:

score: 0
Accepted
time: 525ms
memory: 101284kb

input:

1000000 1000000 900084

output:

651386967

result:

ok answer is '651386967'

Test #31:

score: 0
Accepted
time: 538ms
memory: 101964kb

input:

1000000 1000000 27328

output:

621963453

result:

ok answer is '621963453'

Test #32:

score: 0
Accepted
time: 544ms
memory: 102408kb

input:

1000000 1000000 538409

output:

997879100

result:

ok answer is '997879100'

Test #33:

score: 0
Accepted
time: 518ms
memory: 102232kb

input:

1000000 1000000 928121

output:

964724707

result:

ok answer is '964724707'

Test #34:

score: 0
Accepted
time: 499ms
memory: 85360kb

input:

685624 665877 563708

output:

257429683

result:

ok answer is '257429683'

Test #35:

score: 0
Accepted
time: 526ms
memory: 99000kb

input:

692290 942095 553970

output:

82511143

result:

ok answer is '82511143'

Test #36:

score: 0
Accepted
time: 524ms
memory: 90036kb

input:

579579 765702 631728

output:

954001361

result:

ok answer is '954001361'

Test #37:

score: 0
Accepted
time: 514ms
memory: 82028kb

input:

756854 634736 567170

output:

393747028

result:

ok answer is '393747028'

Test #38:

score: 0
Accepted
time: 544ms
memory: 101568kb

input:

649175 997874 511181

output:

242172216

result:

ok answer is '242172216'

Test #39:

score: 0
Accepted
time: 527ms
memory: 101928kb

input:

786431 1000000 999999

output:

627359027

result:

ok answer is '627359027'