Language: C++

// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using i32 = int32_t;
using i64 = int64_t;
#define int ll
#define double ld
#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define rep1(i,n) for (int i = 1; i <= (int)(n); i++)
#define repR(i,n) for (int i = (int)(n)-1; i >= 0; i--)
#define rep1R(i,n) for (int i = (int)(n); i >= 1; i--)
#define loop(i,a,B) for (int i = a; i B; i++)
#define loopR(i,a,B) for (int i = a; i B; i--)
#define all(x) (x).begin(), (x).end()
#define allR(x) (x).rbegin(), (x).rend()
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fst first
#define snd second
auto constexpr INF32 = numeric_limits<int32_t>::max()/2-1;
auto constexpr INF64 = numeric_limits<int64_t>::max()/2-1;
auto constexpr INF   = numeric_limits<int>::max()/2-1;
#ifdef LOCAL
#include "debug.hpp"
#define dump(...) cerr << "[" << setw(3) << __LINE__ << ":" << __FUNCTION__ << "] ", dump_impl(#__VA_ARGS__, __VA_ARGS__)
#define say(x) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] " << x << endl
#define debug if (1)
#else
#define dump(...) (void)(0)
#define say(x) (void)(0)
#define debug if (0)
#endif
template <class T> using pque_max = priority_queue<T>;
template <class T> using pque_min = priority_queue<T, vector<T>, greater<T> >;
template <class T, class = typename T::iterator, class = typename enable_if<!is_same<T, string>::value>::type>
ostream& operator<<(ostream& os, T const& v) { bool f = true; for (auto const& x : v) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, class = typename T::iterator, class = typename enable_if<!is_same<T, string>::value>::type>
istream& operator>>(istream& is, T &v) { for (auto& x : v) is >> x; return is; }
template <class T, class S> istream& operator>>(istream& is, pair<T,S>& p) { return is >> p.first >> p.second; }
struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup;
template <class F> struct FixPoint : private F {
    constexpr FixPoint(F&& f) : F(forward<F>(f)) {}
    template <class... T> constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward<T>(x)...); }
};
struct MakeFixPoint {
    template <class F> constexpr auto operator|(F&& f) const { return FixPoint<F>(forward<F>(f)); }
};
#define MFP MakeFixPoint()|
#define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__)
template <class T, size_t d> struct vec_impl {
    using type = vector<typename vec_impl<T,d-1>::type>;
    template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T,d-1>::make_v(forward<U>(x)...)); }
};
template <class T> struct vec_impl<T,0> { using type = T; static type make_v(T const& x = {}) { return x; } };
template <class T, size_t d = 1> using vec = typename vec_impl<T,d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T,d>::make_v(forward<Args>(args)...); }
template <class T> void quit(T const& x) { cout << x << endl; exit(0); }
template <class T> constexpr bool chmin(T& x, T const& y) { if (x > y) { x = y; return true; } return false; }
template <class T> constexpr bool chmax(T& x, T const& y) { if (x < y) { x = y; return true; } return false; }
template <class It> constexpr auto sumof(It b, It e) { return accumulate(b,e,typename iterator_traits<It>::value_type{}); }
template <class T> int sz(T const& x) { return x.size(); }
template <class C, class T> int lbd(C const& v, T const& x) {
    return lower_bound(v.begin(), v.end(), x)-v.begin();
}
template <class C, class T> int ubd(C const& v, T const& x) {
    return upper_bound(v.begin(), v.end(), x)-v.begin();
}
template <class C, class F> int ppt(C const& v, F f) {
    return partition_point(v.begin(), v.end(), f)-v.begin();
}
// <<<
// >>> NTT
template <class ModInt, int64_t g>
struct NTT {
    using modint = ModInt;
    static constexpr int64_t mod = ModInt::mod, gen = g, max_lg = __builtin_ctzll(mod-1);
    // mod:prime, g:primitive root
    static_assert(mod > 0 && g > 0 && max_lg > 0, "");

    using arr_t = array<ModInt,max_lg+1>;
    static arr_t ws,iws;
    static void init() {
        for (int i = 0; i <= max_lg; i++) {
            ws[i] = -ModInt(g).pow((mod-1)>>(i+2));
            iws[i] = ModInt(1)/ws[i];
        }
    }
    static void ntt(ModInt a[], int lg) {
        for (int b = lg-1; b >= 0; b--) {
            ModInt w = 1;
            for (int i = 0, k = 0; i < (1<<lg); i += 1<<(b+1)) {
                for (int j = i; j < (i|(1<<b)); j++) {
                    const int k = j|(1<<b);
                    const auto x = a[j], y = a[k];
                    a[j] = x + y*w;
                    a[k] = x - y*w;
                }
                w *= ws[__builtin_ctz(++k)];
            }
        }
//        bit_reverse(a,1<<lg);
    }
    static void intt(ModInt a[], int lg) {
//        bit_reverse(a,1<<lg);
        for (int b = 0; b < lg; b++) {
            ModInt w = 1;
            for (int i = 0, k = 0; i < (1<<lg); i += 1<<(b+1)) {
                for (int j = i; j < (i|(1<<b)); j++) {
                    const int k = j|(1<<b);
                    const auto x = a[j], y = a[k];
                    a[j] = x + y;
                    a[k] = w*(x - y);
                }
                w *= iws[__builtin_ctz(++k)];
            }
        }
    }
    template <class T>
    static vector<ModInt> conv(vector<T> const& a, vector<T> const& b) {
        if (a.empty() || b.empty()) return {};
        init();
        const int s = a.size() + b.size() - 1, lg = __lg(2*s-1);
        assert(lg <= max_lg);

        vector<ModInt> aa(1<<lg);
        rep (i,a.size()) aa[i] = (int)a[i];
        ntt(aa.data(), lg);

        vector<ModInt> bb(1<<lg);
        rep (i,b.size()) bb[i] = (int)b[i];
        ntt(bb.data(), lg);

        const auto x = ModInt(1)/ModInt(1<<lg);
        rep (i,1<<lg) aa[i] *= bb[i]*x;
        intt(aa.data(), lg); aa.resize(s);
        return aa;
    }
    template <class T>
    static vector<ModInt> conv(vector<T> const& a) {
        if (a.empty()) return {};
        init();
        const int s = a.size()*2 - 1, lg = __lg(2*s-1);
        assert(lg <= max_lg);

        vector<ModInt> aa(1<<lg);
        rep (i,a.size()) aa[i] = (int)a[i];
        ntt(aa.data(), lg);

        const auto x = ModInt(1)/ModInt(1<<lg);
        rep (i,1<<lg) aa[i] *= aa[i]*x;
        intt(aa.data(), lg); aa.resize(s);
        return aa;
    }
};
template <class ModInt, int64_t g>
typename NTT<ModInt,g>::arr_t NTT<ModInt,g>::ws;
template <class ModInt, int64_t g>
typename NTT<ModInt,g>::arr_t NTT<ModInt,g>::iws;
// <<<

// >>> modint
template <uint32_t MOD>
struct modint {
    using u32 = uint32_t;
    using u64 = uint64_t;
    using i64 = int64_t;
    using M = modint;

    static constexpr u32 mul_inv(u32 n, int e = 5, u32 x = 1) {
        return e == 0 ? x : mul_inv(n, e-1, x*(2-x*n));
    }
    static constexpr u32 mod = MOD;
    static constexpr u32 nn = mul_inv(MOD);
    static constexpr u32 r2 = -u64(MOD) % MOD;

    u32 x;
    constexpr modint(i64 x = 0) : x(reduce(((x%=MOD)<0 ? x+MOD : x)*r2)) {}
    static constexpr u32 reduce(u64 w) {
        return u32(w >> 32) + MOD - i64((u64(u32(w) * nn) * MOD) >> 32);
    }
    constexpr i64 val() const {
        i64 r = reduce(x);
        if (r >= MOD) r -= MOD;
        return r;
    }
    constexpr explicit operator i64() const { return val(); }
    constexpr bool operator==(M p) const { return val() == p.val(); }
    constexpr bool operator!=(M p) const { return val() != p.val(); }
    constexpr M operator+() const { return *this; }
    constexpr M operator-() const { M r; r.x = x ? i64(2*MOD)-x : 0; return r; }
    constexpr M &operator+=(M p) {
        i64 t = x; if (((t += p.x) -= 2*MOD) < 0) t += 2*MOD;
        x = t;
        return *this;
    }
    constexpr M &operator-=(M p) { return *this += -p; }
    constexpr M &operator*=(M p) { x = reduce(u64(x)*p.x); return *this; }
    constexpr M &operator/=(M p) { *this *= p.inv(); return *this; }

    constexpr M operator+(M p) const { return M(*this) += p; }
    constexpr M operator-(M p) const { return M(*this) -= p; }
    constexpr M operator*(M p) const { return M(*this) *= p; }
    constexpr M operator/(M p) const { return M(*this) /= p; }
    friend constexpr M operator+(i64 x, M y) { return M(x)+y; }
    friend constexpr M operator-(i64 x, M y) { return M(x)-y; }
    friend constexpr M operator*(i64 x, M y) { return M(x)*y; }
    friend constexpr M operator/(i64 x, M y) { return M(x)/y; }

    constexpr M inv() const { return pow(MOD - 2); }
    constexpr M pow(i64 n) const {
        if (n < 0) return inv().pow(-n);
        M v = *this, r = 1;
        for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v;
        return r;
    }

    friend ostream &operator<<(ostream &os, M p) {
        return os << p.val();
    }
    friend istream &operator>>(istream &is, M &a) {
        u32 t; is >> t; a = t; return is;
    }
#ifdef LOCAL
    friend string to_s(M p) { return to_s(p.val(), MOD); }
#endif
};
// <<<
constexpr int64_t MOD = 1e9+7;
using mint = modint<MOD>;

// >>> garner, convolution for arbitray mod
using ntt1 = NTT<modint< 167772161>, 3>; // mod-1 =  5<<25
using ntt2 = NTT<modint< 469762049>, 3>; // mod-1 =  7<<26
using ntt3 = NTT<modint<1224736769>, 3>; // mod-1 = 73<<24
//using ntt3 = NTT<modint<998244353>, 3>; // mod-1 = 119<<23

// https://math314.hateblo.jp/entry/2015/05/07/014908
template <class ModInt, class P, class Q, class R>
constexpr ModInt garner(P const& x, Q const& y, R const& z) {
    using ll = int64_t;
    const ll xx = (ll)x, yy = (ll)y, zz = (ll)z;
    constexpr ll m1 = ntt1::mod, m2 = ntt2::mod;
	constexpr auto m1_inv_m2 = ntt2::modint(m1).inv();
	constexpr auto m12_inv_m3 = ntt3::modint(m1 * m2).inv();
	constexpr auto m12_mod = ModInt(m1 * m2);
    auto v1 = (yy - xx) * m1_inv_m2;
    auto v2 = (zz - (xx + m1 * v1.val())) * m12_inv_m3;
    return xx + m1 * v1.val() + m12_mod * ModInt(v2.val());
}
template <class ModInt>
vector<ModInt> conv(vector<ModInt> const& a, vector<ModInt> const& b) {
    auto x = ntt1::conv(a, b);
    auto y = ntt2::conv(a, b);
    auto z = ntt3::conv(a, b);
	vector<ModInt> ret(x.size());
	rep (i,x.size()) ret[i] = garner<ModInt>(x[i],y[i],z[i]);
    return ret;
}
template <class ModInt>
vector<ModInt> conv(vector<ModInt> const& a) {
    auto x = ntt1::conv(a);
    auto y = ntt2::conv(a);
    auto z = ntt3::conv(a);
	vector<ModInt> ret(x.size());
	rep (i,x.size()) ret[i] = garner<ModInt>(x[i],y[i],z[i]);
    return ret;
}
// <<<

using FPS = vector<mint>;
// FPS operator*(FPS const& x, FPS const& y) {
//     FPS z(x.size()+y.size()-1);
//     rep (i,x.size()) rep (j,y.size()) z[i+j] += x[i]*y[j];
//     return z;
// }
// void operator*=(FPS &x, FPS const& y) {
//     static FPS z;
//     z.assign(x.size()+y.size()-1,0);
//     rep (i,x.size()) rep (j,y.size()) z[i+j] += x[i]*y[j];
//     swap(x,z);
// }
void operator*=(FPS &x, FPS const& y) {
    x = conv(x,y);
}

int32_t main() {
    int n; cin >> n;
    string s; cin >> s;

    auto dp0 = make_v<mint,2>(n+1,n+1);
    dp0[0][0] = 1;
    rep (j,n) rep (i,n+1) {
        if (i+2 < n+1) dp0[i+1][j+1] += 2*dp0[i][j];
        if (i-1 >= 0) dp0[i-1][j+1] += dp0[i][j];
    }
    dump(as_mat(dp0));

    auto dp1 = make_v<mint,2>(n+1,n+1);
    dp1[0][0] = 1;
    rep (j,n) rep (i,n+1) {
        if (i+2 < n+1) dp1[i+1][j+1] += 2*dp1[i][j];
        dp1[max(0LL,i-1)][j+1] += dp1[i][j];
    }
    dump(as_mat(dp1));

    const int m = s.size();
    FPS res = dp1[0], p = dp0[0];
    for (int k = m; k; k >>= 1) {
        if (k&1) {
            res *= p;
            res.resize(n-m+1);
        }
        p *= p;
        p.resize(n-m+1);
    }
    dump(res);

    cout << res[n-m] << endl;


}


Compiler output:
a.cc: In instantiation of 'static std::vector<_Tp> NTT<ModInt, g>::conv(const std::vector<T>&, const std::vector<T>&) [with T = modint<1000000007>; ModInt = modint<167772161>; long int g = 3]':
a.cc:255:24:   required from 'std::vector<_Tp> conv(const std::vector<_Tp>&, const std::vector<_Tp>&) [with ModInt = modint<1000000007>]'
  255 |     auto x = ntt1::conv(a, b);
      |              ~~~~~~~~~~^~~~~~
a.cc:286:13:   required from here
  286 |     x = conv(x,y);
      |         ~~~~^~~~~
a.cc:129:34: error: invalid cast from type 'const __gnu_cxx::__alloc_traits<std::allocator<modint<1000000007> >, modint<1000000007> >::value_type' {aka 'const modint<1000000007>'} to type 'll' {aka 'long long int'}
  129 |         rep (i,a.size()) aa[i] = (int)a[i];
      |                                  ^~~~~~~
a.cc:133:34: error: invalid cast from type 'const __gnu_cxx::__alloc_traits<std::allocator<modint<1000000007> >, modint<1000000007> >::value_type' {aka 'const modint<1000000007>'} to type 'll' {aka 'long long int'}
  133 |         rep (i,b.size()) bb[i] = (int)b[i];
      |                                  ^~~~~~~
a.cc: In instantiation of 'static std::vector<_Tp> NTT<ModInt, g>::conv(const std::vector<T>&, const std::vector<T>&) [with T = modint<1000000007>; ModInt = modint<469762049>; long int g = 3]':
a.cc:256:24:   required from 'std::vector<_Tp> conv(const std::vector<_Tp>&, const std::vector<_Tp>&) [with ModInt = modint<1000000007>]'
  256 |     auto y = ntt2::conv(a, b);
      |              ~~~~~~~~~~^~~~~~
a.cc:286:13:   required from here
  286 |     x = conv(x,y);
      |         ~~~~^~~~~
a.cc:129:34: error: invalid cast from type 'const __gnu_cxx::__alloc_traits<std::allocator<modint<1000000007> >, modint<1000000007> >::value_type' {aka 'const modint<1000000007>'} to type 'll' {aka 'long long int'}
  129 |         rep (i,a.size()) aa[i] = (int)a[i];
      |                                  ^~~~~~~
a.cc:133:34: error: invalid cast from type 'const __gnu_cxx::__alloc_traits<std::allocator<modint<1000000007> >, modint<1000000007> >::value_type' {aka 'const modint<1000000007>'} to type 'll' {aka 'long long int'}
  133 |         rep (i,b.size()) bb[i] = (int)b[i];
      |                                  ^~~~~~~
a.cc: In instantiation of 'static std::vector<_Tp> NTT<ModInt, g>::conv(const std::vector<T>&, const std::vector<T>&) [with T = modint<1000000007>; ModInt = modint<1224736769>; long int g = 3]':
a.cc:257:24:   required from 'std::vector<_Tp> conv(const std::vector<_Tp>&, const std::vector<_Tp>&) [with ModInt = modint<1000000007>]'
  257 |     auto z = ntt3::conv(a, b);
      |              ~~~~~~~~~~^~~~~~
a.cc:286:13:   required from here
  286 |     x = conv(x,y);
      |         ~~~~^~~~~
a.cc:129:34: error: invalid cast from type 'const __gnu_cxx::__alloc_traits<std::allocator<modint<1000000007> >, modint<1000000007> >::value_type' {aka 'const modint<1000000007>'} to type 'll' {aka 'long long int'}
  129 |         rep (i,a.size()) aa[i] = (int)a[i];
      |                                  ^~~~~~~
a.cc:133:34: error: invalid cast from type 'const __gnu_cxx::__alloc_traits<std::allocator<modint<1000000007> >, modint<1000000007> >::value_type' {aka 'const modint<1000000007>'} to type 'll' {aka 'long long int'}
  133 |         rep (i,b.size()) bb[i] = (int)b[i];
      |                                  ^~~~~~~