#include <bits/stdc++.h>

using i64 = long long;

template <typename T> constexpr T power(T a, i64 b) {
    T c{1}; for (; b; b /= 2, a *= a) if (b & 1) c *= a;
    return c;
}
template <int P> struct MInt {
    int x;
    constexpr MInt() : x{} {}
    constexpr MInt(i64 x_) : x{norm(x_ % getMod())} {}
    static int Mod;
    constexpr static int getMod() { return P > 0 ? P : Mod; }
    constexpr static void setMod(int Mod_) { Mod = Mod_; }
    constexpr int up(int x) const {
        if (x < 0) x += getMod();
        return x;
    }
    constexpr int down(int x) const {
        if (x >= getMod()) x -= getMod();
        return x;
    }
    constexpr int norm(int x) const {
        return up(down(x));
    }
    constexpr int val() const { return x; }
    explicit constexpr operator int() const { return x; }
    constexpr MInt operator-() const {
        MInt res; res.x = norm(getMod() - x); return res;
    }
    constexpr MInt inv() const {
        assert(x != 0);
        return power(*this, getMod() - 2);
    }
    constexpr MInt &operator+=(MInt rhs) & { return x = down(x + rhs.x), *this; }
    constexpr MInt &operator-=(MInt rhs) & { return x = up(x - rhs.x), *this; }
    constexpr MInt &operator*=(MInt rhs) & { return x = 1ll * x * rhs.x % getMod(), *this; }
    constexpr MInt &operator/=(MInt rhs) & { return *this *= rhs.inv(); }
    friend constexpr MInt operator+(MInt lhs, MInt rhs) { return lhs += rhs; }
    friend constexpr MInt operator-(MInt lhs, MInt rhs) { return lhs -= rhs; }
    friend constexpr MInt operator*(MInt lhs, MInt rhs) { return lhs *= rhs; }
    friend constexpr MInt operator/(MInt lhs, MInt rhs) { return lhs /= rhs; }
    friend constexpr bool operator==(MInt lhs, MInt rhs) { return lhs.val() == rhs.val(); }
    friend constexpr bool operator!=(MInt lhs, MInt rhs) { return lhs.val() != rhs.val(); }
    friend constexpr std::istream &operator>>(std::istream &is, MInt &a) {
        i64 x = 0; is >> x, a = MInt(x); return is;
    }
    friend constexpr std::ostream &operator<<(std::ostream &os, const MInt &a) {
        return os << a.val();
    }
};

template <int P> int MInt<P>::Mod = P;
template <> int MInt<0>::Mod = 998244353;
template <int V, int P> constexpr MInt<P> CInv = MInt<P>(V).inv();

constexpr int P = 998244353;
using Z = MInt<P>;

void solve() {
    std::string s;
    std::cin >> s;
    int n = int(s.size());

    int k;
    std::cin >> k;

    std::vector<int> z(n);
    z[0] = n;
    for (int i = 1, l = 0, r = 0; i < n; ++i) {
        z[i] = std::max(std::min(r - i, z[i - l]), 0);
        while (i + z[i] < n && s[z[i]] == s[i + z[i]]) {
            ++z[i];
        }
        if (i + z[i] > r) {
            l = i;
            r = i + z[i];
        }
    }

    std::vector<int> a(n + 1);
    for (int i = 0; i < n; ++i) {
        if (z[i] >= i && 2 * i + k <= n) {
            a[2 * i + k] += 1;
            int x = std::min(z[i] - i, n - 2 * i) / k * k + 2 * i;
            if (x + k <= n) {
                a[x + k] -= 1;
            }
        }
    }

    Z ans = 1;
    for (int i = 1; i <= n; ++i) {
        if (i + k <= n) {
            a[i + k] += a[i];
        }
        ans *= a[i] + 1;
    }

    std::cout << ans << "\n";
}

int main() {
    std::cin.tie(nullptr)->sync_with_stdio(false);

    int t;
    std::cin >> t;

    while (t--) {
        solve();
    }

    return 0;
}