Problem p02632 (C++) — buggy submission, verdict: Time Limit Exceeded

//
//                               S i r o t a n   w a t c h e s   o v e r   y o u
//                               .
//
//                                          ...Jggg+J+JJJg@NQmgJa.....,
//                                 ....gH@@@@HHB""""7"YYYYHMMMMMMM@@@@@@@Hma,.
//                            ...JH@@MMHY"!                        ?
//                            __""YH@@@@N&...
//                        ..JH@@HY"~ _TW@@@Mme.
//                     .Jg@@#"= _TTM@@N..
//                  .Jg@@MY! ?T@@@h,.
//                .-@@@B! (TM@@@L
//              .(H@MY ?W@@@+
//             .W@@@ .T@@@[
//           .d@@M! .T@@N,
//          .d@M@' -W@@o.
//         (@@M\\ ?M@N,
//        -d@M%                    ..,                                      ..,
//        j@@b
//       d@@M=                     TM9                                      ?MD
//       W@@[
//      .H@M: .W@H, H@Ht ,@@#
//     (@@M~ .@@h.
//    .@@M%                        ..gmHHJ.                             .JdHga.
//    .H@@e
//    j@@#_                       .@@@@@@@b J@@@@@@@h. .H@@\\  d@@@ .4@@@@@@MF
//    (@@@@@@@@                        H@@b d@@[                         ?"BMY"=
//    .d@@@@H,          ?TWHHY"!                        d@@e J@@b .JJJ-..,
//    ,@@@@@@M%                       .........         -@@@M.
//    ?@@M\\         ?YHHM@@@@b                ..      .W@@HP X@@HMWY"= d@@@#
//    ,@@@L.                                 ?H@Ng&+gd@@#H@@NHaJ+gH@[ J@@@]
//     X@@@[            ......                 ?"YYYYY""   ?"YHHHB"^ ..... (@@@#
//      WH@N+.      .W@@@@MHB= .TWH@M@Hmc       .H@@M~
//     .H@@@@N,      _!~ .d@@@N,
//   .J@@#T@@@N, .d@@@@@@@b.
//  (@@@@! .T@@@n, .(H@@@H>.W@@@x
// (@@@F      4@@@@MaJ. .d@@@@Y77   4@@@r
//.H@@P         ?TM@@@@N... .-JH@HMY=        d@@N,
//(@@@F             ?"WM@@@MQa-,. .(J(JN@@M#"             Z@@@L
// d@@H,                 (M@@@@@@@Ng&maJ....                           ..
// ...J.J+W@@@@@@HY!               .dH@b ?M@@@N&.
// ..(JW@@@MM"?7""TYHMH@@HH@@@@@HHHgkHagHa(mggdmmagH@H@@Q@@HMMMHY"7!TMM@@@HaJ,.
// ..H@@@M^
//   ?"W@@@@MN@@@@@H@@MMY"                  _???!"= ?WMMBYYTMH=7""Y@""?"~^
//   _"YM@@@@@@@@MH@@@@@#"^
//       ?77WMMMYB""! _7"WWMMMY"7=

// need
#include <algorithm>
#include <iostream>
// data structure
#include <bitset>
#include <complex>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
// #include <deque>
#include <array>
#include <unordered_map>
#include <unordered_set>
#include <valarray>
// etc
#include <cassert>
#include <chrono>
#include <cmath>
#include <fstream>
#include <functional>
#include <iomanip>
#include <numeric>
#include <random>

auto &scan_in = std::cin;

// input
#define INIT                                                                   \\
  std::ios::sync_with_stdio(false);                                            \\
  std::cin.tie(0);
#define VAR(type, ...)                                                         \\
  type __VA_ARGS__;                                                            \\
  MACRO_VAR_Scan(__VA_ARGS__);
template <typename T> void MACRO_VAR_Scan(T &t) { scan_in >> t; }
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First &first, Rest &...rest) {
  scan_in >> first;
  MACRO_VAR_Scan(rest...);
}
#define VEC_ROW(type, n, ...)                                                  \\
  std::vector<type> __VA_ARGS__;                                               \\
  MACRO_VEC_ROW_Init(n, __VA_ARGS__);                                          \\
  for (int w_ = 0; w_ < n; ++w_) {                                             \\
    MACRO_VEC_ROW_Scan(w_, __VA_ARGS__);                                       \\
  }
template <typename T> void MACRO_VEC_ROW_Init(int n, T &t) { t.resize(n); }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Init(int n, First &first, Rest &...rest) {
  first.resize(n);
  MACRO_VEC_ROW_Init(n, rest...);
}
template <typename T> void MACRO_VEC_ROW_Scan(int p, T &t) { scan_in >> t[p]; }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Scan(int p, First &first, Rest &...rest) {
  scan_in >> first[p];
  MACRO_VEC_ROW_Scan(p, rest...);
}
#define VEC(type, c, n)                                                        \\
  std::vector<type> c(n);                                                      \\
  for (auto &i : c)                                                            \\
    scan_in >> i;
#define MAT(type, c, m, n)                                                     \\
  std::vector<std::vector<type>> c(m, std::vector<type>(n));                   \\
  for (auto &R : c)                                                            \\
    for (auto &w : R)                                                          \\
      scan_in >> w;
// output
template <typename T> void MACRO_OUT(const T t) { std::cout << t; }
template <typename First, typename... Rest>
void MACRO_OUT(const First first, const Rest... rest) {
  std::cout << first << " ";
  MACRO_OUT(rest...);
}
#define OUT(...) MACRO_OUT(__VA_ARGS__);
#define FOUT(n, dist) std::cout << std::fixed << std::setprecision(n) << (dist);
#define SOUT(n, c, dist) std::cout << std::setw(n) << std::setfill(c) << (dist);
#define VOUT(v)                                                                \\
  for (size_t i = 0; i < v.size(); ++i) {                                      \\
    OUT(v[i]);                                                                 \\
    if (i + 1 < v.size()) {                                                    \\
      SP                                                                       \\
    }                                                                          \\
  }
#define EOUT(...)                                                              \\
  do {                                                                         \\
    OUT(__VA_ARGS__) BR;                                                       \\
    exit(0);                                                                   \\
  } while (0);
#define SP std::cout << " ";
#define TAB std::cout << "\\t";
#define BR std::cout << "\\n";
#define SPBR(w, n) std::cout << (w + 1 == n ? '\\n' : ' ');
#define ENDL std::cout << std::endl;
#define FLUSH std::cout << std::flush;
#define SHOW(dist)                                                             \\
  { std::cerr << #dist << "\\t: " << (dist) << "\\n"; }
// utility
#define ALL(a) (a).begin(), (a).end()
#define FOR(w, a, n) for (int w = (a); w < (n); ++w)
#define REP(w, n) FOR(w, 0, n)
#define RFOR(w, a, n) for (int w = (n)-1; w >= (a); --w)
#define RREP(w, n) RFOR(w, 0, n)
template <class S, class T, class U> bool IN(S a, T x, U b) {
  return a <= x && x < b;
}
template <class T> inline T CHMAX(T &a, const T b) {
  return a = (a < b) ? b : a;
}
template <class T> inline T CHMIN(T &a, const T b) {
  return a = (a > b) ? b : a;
}
// test
template <class T> using V = std::vector<T>;
template <class T> using VV = V<V<T>>;

template <typename S, typename T>
std::ostream &operator<<(std::ostream &os, const std::pair<S, T> &p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
  os << "{";
  for (size_t i = 0; i < v.size(); ++i)
    os << v[i] << ((i + 1 < v.size()) ? ", " : "}");
  return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, std::queue<T> q) {
  os << "<";
  while (!q.empty()) {
    os << q.front();
    q.pop();
    os << (q.empty() ? "<" : ", ");
  }
  return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, std::stack<T> q) {
  os << ">";
  while (!q.empty()) {
    os << q.top();
    q.pop();
    os << (q.empty() ? "]" : ", ");
  }
  return os;
}
namespace std {
template <typename S, typename T> class numeric_limits<pair<S, T>> {
public:
  static constexpr pair<S, T> max() noexcept {
    return {numeric_limits<S>::max(), numeric_limits<T>::max()};
  }
  static constexpr pair<S, T> lowest() noexcept {
    return {numeric_limits<S>::lowest(), numeric_limits<T>::lowest()};
  }
};
} // namespace std

// type/const
using i64 = std::int_fast64_t;
using u64 = std::uint_fast64_t;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PAIR = std::pair<i64, i64>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = (1 << 30) - 1;                   // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;             // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                         // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18
constexpr double EPS = 1e-6;
constexpr i64 MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;
template <class T, size_t N> void FILL(T (&a)[N], const T &val) {
  for (auto &x : a)
    x = val;
}
template <class ARY, size_t N, size_t M, class T>
void FILL(ARY (&a)[N][M], const T &val) {
  for (auto &b : a)
    FILL(b, val);
}
template <class T> void FILL(std::vector<T> &a, const T &val) {
  for (auto &x : a)
    x = val;
}
template <class ARY, class T>
void FILL(std::vector<std::vector<ARY>> &a, const T &val) {
  for (auto &b : a)
    FILL(b, val);
}
// ------------>8---------

ll powMod(ll n, ll p, ll mod) {
  ll res = 1;
  while (p) {
    if (p & 1)
      (res *= n) %= mod;
    (n *= n) %= mod;
    p >>= 1;
  }
  return res;
}
ll invMod(ll n, ll mod) { return powMod(n, MOD - 2, MOD); }

const signed FACT_MAX_N = 3000006;
signed fact[FACT_MAX_N];
signed factInv[FACT_MAX_N];
struct INIT_FACT {
  INIT_FACT() {
    fact[0] = 1;
    for (int i = 1; i < FACT_MAX_N; ++i)
      fact[i] = (long long)i * fact[i - 1] % MOD;
    factInv[FACT_MAX_N - 1] = powMod(fact[FACT_MAX_N - 1], MOD - 2, MOD);
    for (int i = FACT_MAX_N - 2; i >= 0; --i)
      factInv[i] = (long long)(i + 1) * factInv[i + 1] % MOD;
  }
} init_fact;

#if true // true if use MOD
/* n,r<=10^6, query O(1)*/
ll Permutation(int n, int r) {
  if (r == 0)
    return 1;
  if (n < r)
    return 0;
  return (long long)fact[n] * factInv[n - r] % MOD;
}
ll Combination(int n, int r) {
  if (r == 0)
    return 1;
  if (n < r)
    return 0;
  return (long long)fact[n] * factInv[n - r] % MOD * factInv[r] % MOD;
}
ll CombinationWithRepetition(ll n, ll r) { return Combination(n + r - 1, r); }
/*n<=10^9, r<=10^5, query O(r)*/
/*ll Combination(ll n, ll r, ll mod) {
        if (n < r) return 0;
        ll ans = 1;
        if (n < 2 * r) r = n - r;
        for (int i = 1; i <= r; ++i) {
                ans *= n - i + 1; ans %= mod;
                ans *= powMod(i, mod - 2, mod); ans %= mod;
        }
        return ans;
}
ll Permutation(int n, int r, int mod) {
        return Combination(n, r, mod) * fact[r] % MOD;
}*/
#else // unuse MOD
const signed COMB_MAX_N = 67; // <- max : 67
long long comb[COMB_MAX_N][COMB_MAX_N];
struct INIT_COMB {
  INIT_COMB() {
    for (int i = 0; i < COMB_MAX_N; ++i) {
      for (int j = 0; j <= i; ++j) {
        if (j == 0 || j == i)
          comb[i][j] = 1;
        else
          comb[i][j] = comb[i - 1][j - 1] + comb[i - 1][j];
      }
    }
  }
} init_comb;
#endif

signed main() {
  INIT;

  VAR(int, k);
  VAR(std::string, s);

  // sum_{|s|<=i<=|s|+k} [x^i](x + 25) ^ (|s|+k)
  i64 ans = 0;
  FOR(i, s.size(), s.size() + k + 1) {
    (ans += Combination(s.size() + k, i) * powMod(25, s.size() + k - i, MOD)) %=
        MOD;
  }
  OUT(ans) BR;

  return 0;
}

Error: TLE

Fixed submission:

//
//                               S i r o t a n   w a t c h e s   o v e r   y o u
//                               .
//
//                                          ...Jggg+J+JJJg@NQmgJa.....,
//                                 ....gH@@@@HHB""""7"YYYYHMMMMMMM@@@@@@@Hma,.
//                            ...JH@@MMHY"!                        ?
//                            __""YH@@@@N&...
//                        ..JH@@HY"~ _TW@@@Mme.
//                     .Jg@@#"= _TTM@@N..
//                  .Jg@@MY! ?T@@@h,.
//                .-@@@B! (TM@@@L
//              .(H@MY ?W@@@+
//             .W@@@ .T@@@[
//           .d@@M! .T@@N,
//          .d@M@' -W@@o.
//         (@@M\\ ?M@N,
//        -d@M%                    ..,                                      ..,
//        j@@b
//       d@@M=                     TM9                                      ?MD
//       W@@[
//      .H@M: .W@H, H@Ht ,@@#
//     (@@M~ .@@h.
//    .@@M%                        ..gmHHJ.                             .JdHga.
//    .H@@e
//    j@@#_                       .@@@@@@@b J@@@@@@@h. .H@@\\  d@@@ .4@@@@@@MF
//    (@@@@@@@@                        H@@b d@@[                         ?"BMY"=
//    .d@@@@H,          ?TWHHY"!                        d@@e J@@b .JJJ-..,
//    ,@@@@@@M%                       .........         -@@@M.
//    ?@@M\\         ?YHHM@@@@b                ..      .W@@HP X@@HMWY"= d@@@#
//    ,@@@L.                                 ?H@Ng&+gd@@#H@@NHaJ+gH@[ J@@@]
//     X@@@[            ......                 ?"YYYYY""   ?"YHHHB"^ ..... (@@@#
//      WH@N+.      .W@@@@MHB= .TWH@M@Hmc       .H@@M~
//     .H@@@@N,      _!~ .d@@@N,
//   .J@@#T@@@N, .d@@@@@@@b.
//  (@@@@! .T@@@n, .(H@@@H>.W@@@x
// (@@@F      4@@@@MaJ. .d@@@@Y77   4@@@r
//.H@@P         ?TM@@@@N... .-JH@HMY=        d@@N,
//(@@@F             ?"WM@@@MQa-,. .(J(JN@@M#"             Z@@@L
// d@@H,                 (M@@@@@@@Ng&maJ....                           ..
// ...J.J+W@@@@@@HY!               .dH@b ?M@@@N&.
// ..(JW@@@MM"?7""TYHMH@@HH@@@@@HHHgkHagHa(mggdmmagH@H@@Q@@HMMMHY"7!TMM@@@HaJ,.
// ..H@@@M^
//   ?"W@@@@MN@@@@@H@@MMY"                  _???!"= ?WMMBYYTMH=7""Y@""?"~^
//   _"YM@@@@@@@@MH@@@@@#"^
//       ?77WMMMYB""! _7"WWMMMY"7=

// need
#include <algorithm>
#include <iostream>
// data structure
#include <bitset>
#include <complex>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
// #include <deque>
#include <array>
#include <unordered_map>
#include <unordered_set>
#include <valarray>
// etc
#include <cassert>
#include <chrono>
#include <cmath>
#include <fstream>
#include <functional>
#include <iomanip>
#include <numeric>
#include <random>

auto &scan_in = std::cin;

// input
#define INIT                                                                   \\
  std::ios::sync_with_stdio(false);                                            \\
  std::cin.tie(0);
#define VAR(type, ...)                                                         \\
  type __VA_ARGS__;                                                            \\
  MACRO_VAR_Scan(__VA_ARGS__);
template <typename T> void MACRO_VAR_Scan(T &t) { scan_in >> t; }
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First &first, Rest &...rest) {
  scan_in >> first;
  MACRO_VAR_Scan(rest...);
}
#define VEC_ROW(type, n, ...)                                                  \\
  std::vector<type> __VA_ARGS__;                                               \\
  MACRO_VEC_ROW_Init(n, __VA_ARGS__);                                          \\
  for (int w_ = 0; w_ < n; ++w_) {                                             \\
    MACRO_VEC_ROW_Scan(w_, __VA_ARGS__);                                       \\
  }
template <typename T> void MACRO_VEC_ROW_Init(int n, T &t) { t.resize(n); }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Init(int n, First &first, Rest &...rest) {
  first.resize(n);
  MACRO_VEC_ROW_Init(n, rest...);
}
template <typename T> void MACRO_VEC_ROW_Scan(int p, T &t) { scan_in >> t[p]; }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Scan(int p, First &first, Rest &...rest) {
  scan_in >> first[p];
  MACRO_VEC_ROW_Scan(p, rest...);
}
#define VEC(type, c, n)                                                        \\
  std::vector<type> c(n);                                                      \\
  for (auto &i : c)                                                            \\
    scan_in >> i;
#define MAT(type, c, m, n)                                                     \\
  std::vector<std::vector<type>> c(m, std::vector<type>(n));                   \\
  for (auto &R : c)                                                            \\
    for (auto &w : R)                                                          \\
      scan_in >> w;
// output
template <typename T> void MACRO_OUT(const T t) { std::cout << t; }
template <typename First, typename... Rest>
void MACRO_OUT(const First first, const Rest... rest) {
  std::cout << first << " ";
  MACRO_OUT(rest...);
}
#define OUT(...) MACRO_OUT(__VA_ARGS__);
#define FOUT(n, dist) std::cout << std::fixed << std::setprecision(n) << (dist);
#define SOUT(n, c, dist) std::cout << std::setw(n) << std::setfill(c) << (dist);
#define VOUT(v)                                                                \\
  for (size_t i = 0; i < v.size(); ++i) {                                      \\
    OUT(v[i]);                                                                 \\
    if (i + 1 < v.size()) {                                                    \\
      SP                                                                       \\
    }                                                                          \\
  }
#define EOUT(...)                                                              \\
  do {                                                                         \\
    OUT(__VA_ARGS__) BR;                                                       \\
    exit(0);                                                                   \\
  } while (0);
#define SP std::cout << " ";
#define TAB std::cout << "\\t";
#define BR std::cout << "\\n";
#define SPBR(w, n) std::cout << (w + 1 == n ? '\\n' : ' ');
#define ENDL std::cout << std::endl;
#define FLUSH std::cout << std::flush;
#define SHOW(dist)                                                             \\
  { std::cerr << #dist << "\\t: " << (dist) << "\\n"; }
// utility
#define ALL(a) (a).begin(), (a).end()
#define FOR(w, a, n) for (int w = (a); w < (n); ++w)
#define REP(w, n) FOR(w, 0, n)
#define RFOR(w, a, n) for (int w = (n)-1; w >= (a); --w)
#define RREP(w, n) RFOR(w, 0, n)
template <class S, class T, class U> bool IN(S a, T x, U b) {
  return a <= x && x < b;
}
template <class T> inline T CHMAX(T &a, const T b) {
  return a = (a < b) ? b : a;
}
template <class T> inline T CHMIN(T &a, const T b) {
  return a = (a > b) ? b : a;
}
// test
template <class T> using V = std::vector<T>;
template <class T> using VV = V<V<T>>;

template <typename S, typename T>
std::ostream &operator<<(std::ostream &os, const std::pair<S, T> &p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
  os << "{";
  for (size_t i = 0; i < v.size(); ++i)
    os << v[i] << ((i + 1 < v.size()) ? ", " : "}");
  return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, std::queue<T> q) {
  os << "<";
  while (!q.empty()) {
    os << q.front();
    q.pop();
    os << (q.empty() ? "<" : ", ");
  }
  return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, std::stack<T> q) {
  os << ">";
  while (!q.empty()) {
    os << q.top();
    q.pop();
    os << (q.empty() ? "]" : ", ");
  }
  return os;
}
namespace std {
template <typename S, typename T> class numeric_limits<pair<S, T>> {
public:
  static constexpr pair<S, T> max() noexcept {
    return {numeric_limits<S>::max(), numeric_limits<T>::max()};
  }
  static constexpr pair<S, T> lowest() noexcept {
    return {numeric_limits<S>::lowest(), numeric_limits<T>::lowest()};
  }
};
} // namespace std

// type/const
using i64 = std::int_fast64_t;
using u64 = std::uint_fast64_t;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PAIR = std::pair<i64, i64>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = (1 << 30) - 1;                   // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;             // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                         // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18
constexpr double EPS = 1e-6;
constexpr i64 MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;
template <class T, size_t N> void FILL(T (&a)[N], const T &val) {
  for (auto &x : a)
    x = val;
}
template <class ARY, size_t N, size_t M, class T>
void FILL(ARY (&a)[N][M], const T &val) {
  for (auto &b : a)
    FILL(b, val);
}
template <class T> void FILL(std::vector<T> &a, const T &val) {
  for (auto &x : a)
    x = val;
}
template <class ARY, class T>
void FILL(std::vector<std::vector<ARY>> &a, const T &val) {
  for (auto &b : a)
    FILL(b, val);
}
// ------------>8---------

// Description:
// 整数列a[i],b[i]から列c[k]=sum{a[i]*b[k-i]}を生成する.任意modに対応.O(NlogN).

namespace NTT {
std::vector<int> tmp;
size_t sz = 1;

template <int m> inline int powMod(int n, ll p) {
  int res = 1;
  while (p) {
    if (p & 1)
      res = (ll)res * n % m;
    n = (ll)n * n % m;
    p >>= 1;
  }
  return (int)res;
}
template <int m> inline int invMod(int n) { return powMod<m>(n, m - 2); }

template <int Mod, int PrimitiveRoot> struct NTTPart {
  static std::vector<int> ntt(std::vector<int> a, bool inv = false) {
    size_t mask = sz - 1;
    size_t p = 0;
    for (size_t i = sz >> 1; i >= 1; i >>= 1) {
      auto &cur = (p & 1) ? tmp : a;
      auto &nex = (p & 1) ? a : tmp;
      assert((ll)(Mod - 1) / sz * i < Mod - 1);
      int e = powMod<Mod>(PrimitiveRoot, (Mod - 1) / sz * i);
      if (inv)
        e = invMod<Mod>(e);
      int w = 1;
      for (size_t j = 0; j < sz; j += i) {
        for (size_t k = 0; k < i; ++k) {
          nex[j + k] = (cur[((j << 1) & mask) + k] +
                        (ll)w * cur[(((j << 1) + i) & mask) + k]) %
                       Mod;
        }
        w = (ll)w * e % Mod;
      }
      ++p;
    }
    if (p & 1)
      std::swap(a, tmp);
    if (inv) {
      int invSz = invMod<Mod>(sz);
      for (size_t i = 0; i < sz; ++i)
        a[i] = (ll)a[i] * invSz % Mod;
    }
    return a;
  }
  static std::vector<int> mul(std::vector<int> a, std::vector<int> b) {
    a = ntt(a);
    b = ntt(b);
    for (size_t i = 0; i < sz; ++i)
      a[i] = (ll)a[i] * b[i] % Mod;
    a = ntt(a, true);
    return a;
  }
};

constexpr int M[] = {998244353, 469762049, 167772161};
constexpr int PR[] = {3, 3, 3};
constexpr int NTT_CONVOLUTION_TIME = 3;
/*
        X := max(a)*max(b)*min(|a|, |b|) のとき,
        NTT_CONVOLUTION_TIME <- 1: X <         1224736769 = 1.2*10^ 9 ~ 2^30
        NTT_CONVOLUTION_TIME <- 2: X < 575334854091079681 = 5.8*10^17 ~ 2^59
        NTT_CONVOLUTION_TIME <- 3: X < 2^86 (32bit * 32bit * 10^7くらいまで)
*/

inline void garner(std::vector<int> *c, int mod) {
  if (NTT_CONVOLUTION_TIME == 1) {
    for (auto &x : c[0])
      x %= mod;
  } else if (NTT_CONVOLUTION_TIME == 2) {
    const int r01 = invMod<M[1]>(M[0]);
    for (size_t i = 0; i < sz; ++i) {
      c[1][i] = (c[1][i] - c[0][i]) * (ll)r01 % M[1];
      if (c[1][i] < 0)
        c[1][i] += M[1];
      c[0][i] = (c[0][i] + (ll)c[1][i] * M[0]) % mod;
    }
  } else if (NTT_CONVOLUTION_TIME == 3) {
    const int R01 = invMod<M[1]>(M[0]);
    const int R02 = invMod<M[2]>(M[0]);
    const int R12 = invMod<M[2]>(M[1]);
    const int M01 = (ll)M[0] * M[1] % mod;
    for (size_t i = 0; i < sz; ++i) {
      c[1][i] = (c[1][i] - c[0][i]) * (ll)R01 % M[1];
      if (c[1][i] < 0)
        c[1][i] += M[1];
      c[2][i] = ((c[2][i] - c[0][i]) * (ll)R02 % M[2] - c[1][i]) * R12 % M[2];
      if (c[2][i] < 0)
        c[2][i] += M[2];
      c[0][i] = (c[0][i] + (ll)c[1][i] * M[0] + (ll)c[2][i] * M01) % mod;
    }
  }
}
std::vector<int> mul(std::vector<int> a, std::vector<int> b, int mod) {
  for (auto &x : a)
    x %= mod;
  for (auto &x : b)
    x %= mod;

  size_t m = a.size() + b.size() - 1;
  sz = 1;
  while (m > sz)
    sz <<= 1;
  tmp.resize(sz);
  a.resize(sz, 0);
  b.resize(sz, 0);

  std::vector<int> c[NTT_CONVOLUTION_TIME];
  if (NTT_CONVOLUTION_TIME >= 1)
    c[0] = NTTPart<M[0], PR[0]>::mul(a, b);
  if (NTT_CONVOLUTION_TIME >= 2)
    c[1] = NTTPart<M[1], PR[1]>::mul(a, b);
  if (NTT_CONVOLUTION_TIME >= 3)
    c[2] = NTTPart<M[2], PR[2]>::mul(a, b);
  for (auto &v : c)
    v.resize(m);
  garner(c, mod);
  return c[0];
}
}; // namespace NTT

class Polynomial {
  std::vector<int> coef;

public:
  Polynomial(int N) : coef(N + 1, 0) {}
  Polynomial(std::initializer_list<int> a) : coef(a) {}
  Polynomial &operator+=(const Polynomial &r) {
    if (coef.size() < r.coef.size())
      coef.resize(r.coef.size());
    for (size_t i = 0; i < r.coef.size(); ++i)
      (coef[i] += r.coef[i]) %= MOD;
    return *this;
  }
  Polynomial &operator*=(const Polynomial &r) {
    auto c = NTT::mul(this->coef, r.coef, MOD);
    coef = c;
    return *this;
  }
  Polynomial &operator^=(long long p) {
    Polynomial x(*this);
    *this = Polynomial(0);
    coef[0] = 1;
    while (p) {
      if (p & 1)
        (*this) *= x;
      x *= x;
      p >>= 1;
    }
    return *this;
  }
  int &operator[](size_t i) { return coef[i]; }
};

signed main() {
  INIT;

  VAR(int, k);
  VAR(std::string, s);

  Polynomial p({25, 1});
  p ^= s.size() + k;
  i64 ans = 0;
  FOR(i, s.size(), s.size() + k + 1)(ans += p[i]) %= MOD;
  OUT(ans) BR;

  return 0;
}