Problem p02715 (C++) — buggy submission, verdict: Runtime Error


// #pragma GCC optimize ("-O3")
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <complex>
#include <cstdio>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <regex>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <time.h>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <vector>
#ifdef _MSC_VER
#include <intrin.h>
#define popcnt __popcnt64
// #  define __builtin_popcount __popcnt
#else
#define popcnt __builtin_popcountll
#endif
// #include "boost/variant.hpp"

using namespace std;

typedef long long ll;
constexpr ll MOD = 1000000007LL;
constexpr ll INF = 1LL << 60;

#define rep(i, N, M) for (ll i = N, i##_len = (M); i < i##_len; ++i)
#define rep_skip(i, N, M, ...)                                                 \\
  for (ll i = N, i##_len = (M); i < i##_len; i += (skip))
#define rrep(i, N, M) for (ll i = (M)-1, i##_len = (N - 1); i > i##_len; --i)
#define pb push_back
#define fir first
#define sec second
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define perm(c)                                                                \\
  sort(all(c));                                                                \\
  for (bool c##perm = 1; c##perm;                                              \\
       c##perm = next_permutation(                                             \\
           all(c))) // perm(c){write(c)} writes all permutation of c

typedef pair<double, double> pd;
typedef pair<ll, ll> pll;
typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef vector<pll> vpll;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef vector<string> vs;
template <typename T>
using pq_greater = priority_queue<T, vector<T>, greater<T>>;
template <typename T> using vpt = vector<complex<T>>;

template <int n> struct tll_impl {
  using type = decltype(tuple_cat(tuple<ll>(),
                                  declval<typename tll_impl<n - 1>::type>()));
};
template <> struct tll_impl<1> {
  using type = tuple<ll>;
};
template <int n> using tll = typename tll_impl<n>::type;

template <class T> constexpr ll SZ(T &v) { return static_cast<ll>(v.size()); };

template <int n, typename T> struct vec_t_impl {
  using type = vector<typename vec_t_impl<n - 1, T>::type>;
};
template <typename T> struct vec_t_impl<1, T> {
  using type = vector<T>;
};
template <int n, typename T> using vec_t = typename vec_t_impl<n, T>::type;
// check
static_assert(is_same<vec_t<3, ll>, vector<vector<vector<ll>>>>::value, "");

// decompose vector into basetype and dimension.
template <typename T> struct vec_dec {
  static constexpr int dim = 0;
  using type = T;
};
template <typename T> struct vec_dec<vector<T>> {
  static constexpr int dim = vec_dec<T>::dim + 1;
  using type = typename vec_dec<T>::type;
};
static_assert(is_same<typename vec_dec<vec_t<3, ll>>::type, ll>::value, "");
static_assert(vec_dec<vec_t<3, ll>>::dim == 3, "");

template <typename T = ll> vector<T> makev(size_t a) { return vector<T>(a); }

template <typename T = ll, typename... Ts> auto makev(size_t a, Ts... ts) {
  return vector<decltype(makev<T>(ts...))>(a, makev<T>(ts...));
} // ex:  auto dp =  makev<ll>(4,5) => vector<vector<ll>> dp(4,vector<ll>(5));

template <typename T>
struct is_vector : std::false_type {}; // check if T is vector

template <typename T> struct is_vector<vector<T>> : std::true_type {};
static_assert(is_vector<vector<ll>>::value == true &&
                  is_vector<ll>::value == false,
              "");

// check if T is vector
template <typename T> struct is_pair : std::false_type {};

template <typename T, typename S>
struct is_pair<pair<T, S>> : std::true_type {};
static_assert(is_pair<pll>::value == true && is_pair<ll>::value == false, "");

template <typename T, typename V,
          typename enable_if<!is_vector<T>::value, nullptr_t>::type = nullptr>
void fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V,
          typename enable_if<is_vector<T>::value, nullptr_t>::type = nullptr>
void fill_v(T &t, const V &v) {
  for (auto &&x : t)
    fill_v(x, v);
} // ex:  fill_v(dp, INF);

namespace std {
template <class T> bool operator<(const complex<T> &a, const complex<T> &b) {
  return a.real() == b.real() ? a.imag() < b.imag() : a.real() < b.real();
}
}; // namespace std

template <typename T, typename S>
istream &operator>>(istream &istr, pair<T, S> &x) {
  return istr >> x.first >> x.second;
}
template <typename T> istream &operator>>(istream &istr, vector<T> &x) {
  rep(i, 0, x.size()) istr >> x[i];
  return istr;
}
template <typename T> istream &operator>>(istream &istr, complex<T> &x) {
  T r, i;
  istr >> r >> i;
  x.real(r);
  x.imag(i);
  return istr;
}

template <typename T, typename Delim_t = string,
          typename enable_if<!is_vector<T>::value, nullptr_t>::type = nullptr>
void write(T &x, Delim_t delim = " ") {
  cout << x << delim;
}
template <typename T, typename Delim_t = string,
          typename enable_if<is_vector<T>::value, nullptr_t>::type = nullptr>
void write(T &x, Delim_t delim = " ") {
  rep(i, 0, x.size()) write(x[i], (i == (x.size() - 1) ? "" : delim));
  cout << '\\n';
}

template <typename T> void chmin(T &a, T b) {
  if (a > b)
    a = b;
}
template <typename T> void chmax(T &a, T b) {
  if (a < b)
    a = b;
}

vll seq(ll i, ll j) {
  vll res(j - i);
  rep(k, i, j) res[k] = i + k;
  return res;
}

constexpr ll POW_0(ll x, ll y) {
  if (y == 0)
    return 1;
  if (y == 1)
    return x;
  if (y == 2)
    return x * x;
  if (y % 2 == 0)
    return POW_0(POW_0(x, y / 2), 2LL);
  return ((POW_0(POW_0(x, y / 2), 2LL)) * (x));
}

constexpr ll POW(ll x, ll y, ll mod = 0) {
  if (mod == 0)
    return POW_0(x, y);
  if (y == 0)
    return 1;
  if (y == 1)
    return x % mod;
  if (y == 2)
    return x * x % mod;
  if (y % 2 == 0)
    return POW(POW(x, y / 2, mod), 2LL, mod) % mod;
  return ((POW(POW(x, y / 2, mod), 2LL, mod)) * (x % mod)) % mod;
}

template <typename Inputs, typename Functor,
          typename T = typename Inputs::value_type>
void sort_by(Inputs &inputs, Functor f) {
  std::sort(std::begin(inputs), std::end(inputs),
            [&f](const T &lhs, const T &rhs) { return f(lhs) < f(rhs); });
}

template <typename Inputs, typename Functor,
          typename T = typename Inputs::value_type>
void stable_sort_by(Inputs &inputs, Functor f) {
  std::stable_sort(
      std::begin(inputs), std::end(inputs),
      [&f](const T &lhs, const T &rhs) { return f(lhs) < f(rhs); });
}

template <typename Inputs> void sort_uniq(Inputs &inputs) {
  sort(all(inputs));
  inputs.erase(unique(all(inputs)), inputs.end());
}

vector<string> split(const string &s, char delim) {
  vector<string> elems;
  stringstream ss(s);
  string item;
  if (s.size() > 0 && s.front() == delim) {
    elems.push_back("");
  }
  while (getline(ss, item, delim)) {
    if (!item.empty()) {
      elems.push_back(item);
    }
  }
  if (s.size() > 0 && s.back() == delim) {
    elems.push_back("");
  }
  return elems;
}

template <class T> map<T, ll> inv_map(vector<T> &x) {
  map<T, ll> res;
  rep(i, 0, x.size()) { res[x[i]] = i; }
  return res;
}
template <class T, class val_t = typename T::value_type,
          enable_if_t<!is_same<T, set<val_t>>::value> * = nullptr>
constexpr bool exist(const T &container, val_t val) {
  return find(all(container), val) != container.end();
}
template <class T, class val_t = typename T::value_type,
          enable_if_t<is_same<T, set<val_t>>::value> * = nullptr>
constexpr bool exist(const T &container, val_t val) {
  return container.find(val) != container.end();
}

// inner prod: |a||b|cos(theta)
template <class T> T dot(complex<T> a, complex<T> b) {
  return a.real() * b.real() + a.imag() * b.imag();
}
// outer prod |a||b|sin(theta)
template <class T> T cross(complex<T> a, complex<T> b) {
  return a.real() * b.imag() - a.imag() * b.real();
}

ll div_ferm(ll val, ll b, ll mod) { return (val * POW(b, mod - 2, mod)) % mod; }

// === Modint ===
// static uint_fast64_t runtime_modulus = MOD;

template <ll modulus = MOD> class modint {
public:
  ll val;
  constexpr modint() : val(0) {}
  constexpr modint(ll x) : val((x %= mod()) < 0 ? x + mod() : x) {}
  constexpr modint(ll x, ll modulus_) {
    set_modulo(modulus_);
    val = (x %= mod()) < 0 ? x + mod() : x;
  }
  template <class Ret = ll &>
  static auto modulo() -> std::enable_if_t<(modulus <= 0), Ret> {
    static ll runtime_modulus = numeric_limits<ll>::max();
    return runtime_modulus; // singleton technique
  }
  template <class Ret = const ll>
  static auto mod() -> std::enable_if_t<(modulus <= 0), Ret> {
    return modulo();
  }

  template <class Ret = const ll>
  static constexpr auto mod() -> std::enable_if_t<(modulus > 0), Ret> {
    return modulus;
  }

  template <ll modulus_ = modulus,
            enable_if_t<(modulus_ <= 0), nullptr_t> = nullptr>
  static void set_modulo(ll mod) {
    modulo() = mod;
  }
  void reset_modulo(ll modulus_) {
    modulo() = modulus_;
    val %= mod();
  }
  constexpr modint inv() { return pow(mod() - 2); }
  constexpr ll value() const noexcept { return val; }
  constexpr modint operator+(const modint rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint operator-(const modint rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint operator*(const modint rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint operator/(const modint rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  modint &operator+=(const modint rhs) noexcept {
    val += rhs.val;
    if (val >= mod()) {
      val -= mod();
    }
    return *this;
  }
  modint &operator-=(const modint rhs) noexcept {
    if (val < rhs.val) {
      val += mod();
    }
    val -= rhs.val;
    return *this;
  }
  modint &operator*=(const modint rhs) noexcept {
    val = val * rhs.val % mod();
    return *this;
  }
  modint &operator/=(modint rhs) noexcept {
    ll exp = mod() - 2;
    while (exp) {
      if (exp % 2) {
        *this *= rhs;
      }
      rhs *= rhs;
      exp /= 2;
    }
    return *this;
  }
  modint &operator++() noexcept { return *this += modint(1); }
  modint operator++(int) noexcept {
    modint t = *this;
    *this += modint(1);
    return t;
  }
  modint &operator--() noexcept { return *this -= modint(1); }
  modint operator--(int) noexcept {
    modint t = *this;
    *this -= modint(1);
    return t;
  }
  constexpr modint operator-() { return val ? mod() - val : val; }
  constexpr bool operator==(const modint rhs) const noexcept {
    return val == rhs.value();
  }
  constexpr bool operator!=(const modint rhs) const noexcept {
    return val != rhs.value();
  }
  constexpr bool operator<(const modint rhs) const noexcept {
    return val < rhs.value();
  }
  static constexpr modint zero() { return modint(0); }
  static constexpr modint unit() { return modint(1); }

  modint pow(long long k) const {
    modint v = *this;
    modint res(1), tmp(v);
    while (k) {
      if (k & 1)
        res *= tmp;
      tmp *= tmp;
      k >>= 1;
    }
    return res;
  }

  ll log(modint b) {
    modint val = *this;
    const ll sq = 40000;
    map<modint, ll> dp;
    // dp.reserve(sq);
    modint res(1);
    for (ll r = 0; r < sq; r++) {
      if (!dp.count(res))
        dp[res] = r;
      res *= val;
    }
    modint p = val.inv().pow(sq);
    res = b;
    for (ll q = 0; q <= mod() / sq + 1; q++) {
      if (dp.count(res)) {
        ll idx = q * sq + dp[res];
        if (idx > 0)
          return idx;
      }
      res *= p;
    }
    return INF;
  }
  friend ostream &operator<<(ostream &o, const modint<modulus> &t) {
    o << t.value();
    return o;
  }
  friend istream &operator>>(istream &in, modint<modulus> &t) {
    ll x;
    in >> x;
    t = modint<modulus>(x);
    return in;
  }
  friend modint<modulus> POW(modint<modulus> x, ll n) {
    return modint<modulus>(POW(x.value(), n, mod()));
  }
};
// user defined literal
modint<MOD> operator"" _mod(unsigned long long x) { return modint<MOD>(x); }

class Combination {
  // this calculates combination (nCk).
  // Constructor runs in O(MAX).
  // get(n,k) returns nCk in O(1).

  ll mod, N_MAX;
  vll fac;
  vll finv;
  vll inv;

public:
  Combination(ll mod = MOD, ll N_MAX = 210000)
      : mod(mod), N_MAX(max(N_MAX, (ll)2)), fac(vll(N_MAX + 1)),
        finv(vll(N_MAX + 1)), inv(vll(N_MAX + 1)) {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    pre_process(2LL, N_MAX + 1);
  }

  ll operator()(ll n, ll k) {
    // choose k from n
    if (N_MAX < n)
      pre_process(N_MAX + 1, n + 1);

    if (0 <= n && n < k)
      return 0;
    if (k == 0)
      return 1;
    if (n < 0)
      return operator()(-n + k - 1, k) * (k % 2 ? -1 : 0);
    return fac[n] * (finv[k] * finv[n - k] % mod) % mod;
  }
  ll H(ll n, ll k) {
    // 1) 区間[0, k) を（空を許して）n個に分割する場合の数
    // 2) n個の中からk個を重複を許して選ぶ
    return operator()(n + k - 1, k);
  }
  ll P(ll n, ll k) {
    // n (n-1) ... (n-k+1)
    return (n < k || n < 0) ? 0 : fac[n] * finv[n - k];
  }
  ll Fac(ll n) { return P(n, n); }
  ll FacInv(ll n) { return n < 0 ? 0 : finv[n]; }

private:
  void pre_process(ll m, ll n) {
    if (N_MAX < n) {
      fac.resize(n);
      inv.resize(n);
      finv.resize(n);
    }
    rep(i, m, n) {
      fac[i] = fac[i - 1] * i % mod;
      inv[i] = mod - inv[mod % i] * (mod / i) % mod;
      finv[i] = finv[i - 1] * inv[i] % mod;
    }
  }
};

ll choose(int n, int r) { // O(r) for small n
  ll acc = 1;
  rep(i, 0, r) acc = acc * (n - i) / (i + 1);
  return acc;
}

ll gcd(ll val, ll b) {
  if (val % b == 0)
    return b;
  else
    return gcd(b, val % b);
}

vll divisor(ll n) {
  // returns common divisors in O(sqrt(min(n,m)))
  vll res;
  for (ll i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      res.push_back(i);
      res.push_back(n / i);
    }
    if (i * i == n)
      res.push_back(i);
  }
  sort(res.begin(), res.end());
  return res;
}

vll divisor(ll n, ll m) {
  // returns common divisors in O(sqrt(min(n,m)))
  if (n > m)
    swap(n, m);
  vll res;
  for (ll i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      if (m % i == 0)
        res.push_back(i);
      if (m % (n / i) == 0)
        res.push_back(n / i);
    }
    if (i * i == n && m % i == 0)
      res.push_back(i);
  }
  sort(res.begin(), res.end());
  return res;
}

vpll prime_factorize(ll n) {
  // returns prime factorization of n in O(sprt(n))
  vector<pll> res;
  for (ll p = 2; p * p <= n; ++p) {
    if (n % p != 0)
      continue;
    ll num = 0;
    while (n % p == 0) {
      ++num;
      n /= p;
    }
    res.push_back({p, num});
  }
  if (n != 1)
    res.push_back(make_pair(n, 1));
  return res;
}

int main() {

  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(12);

  ll n, k;
  cin >> n >> k;
  modint<> res = 0;
  vector<modint<>> cnt(k + 1);
  rrep(i, 1, k + 1) {
    cnt[i] = POW(modint<>(k / i), n);
    rep(j, 2, k / i + 1) cnt[i] -= cnt[i * j];
  }
  rep(i, 1, k + 1) { res += cnt[i] * i; }
  cout << res << endl;
  return 0;
}


Error: 0

Fixed submission:


// #pragma GCC optimize ("-O3")
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <complex>
#include <cstdio>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <regex>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <time.h>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <vector>
#ifdef _MSC_VER
#include <intrin.h>
#define popcnt __popcnt64
// #  define __builtin_popcount __popcnt
#else
#define popcnt __builtin_popcountll
#endif
// #include "boost/variant.hpp"

using namespace std;

typedef long long ll;
constexpr ll MOD = 1000000007LL;
constexpr ll INF = 1LL << 60;

#define rep(i, N, M) for (ll i = N, i##_len = (M); i < i##_len; ++i)
#define rep_skip(i, N, M, ...)                                                 \\
  for (ll i = N, i##_len = (M); i < i##_len; i += (skip))
#define rrep(i, N, M) for (ll i = (M)-1, i##_len = (N - 1); i > i##_len; --i)
#define pb push_back
#define fir first
#define sec second
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define perm(c)                                                                \\
  sort(all(c));                                                                \\
  for (bool c##perm = 1; c##perm;                                              \\
       c##perm = next_permutation(                                             \\
           all(c))) // perm(c){write(c)} writes all permutation of c

typedef pair<double, double> pd;
typedef pair<ll, ll> pll;
typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef vector<pll> vpll;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef vector<string> vs;
template <typename T>
using pq_greater = priority_queue<T, vector<T>, greater<T>>;
template <typename T> using vpt = vector<complex<T>>;

template <int n> struct tll_impl {
  using type = decltype(tuple_cat(tuple<ll>(),
                                  declval<typename tll_impl<n - 1>::type>()));
};
template <> struct tll_impl<1> {
  using type = tuple<ll>;
};
template <int n> using tll = typename tll_impl<n>::type;

template <class T> constexpr ll SZ(T &v) { return static_cast<ll>(v.size()); };

template <int n, typename T> struct vec_t_impl {
  using type = vector<typename vec_t_impl<n - 1, T>::type>;
};
template <typename T> struct vec_t_impl<1, T> {
  using type = vector<T>;
};
template <int n, typename T> using vec_t = typename vec_t_impl<n, T>::type;
// check
static_assert(is_same<vec_t<3, ll>, vector<vector<vector<ll>>>>::value, "");

// decompose vector into basetype and dimension.
template <typename T> struct vec_dec {
  static constexpr int dim = 0;
  using type = T;
};
template <typename T> struct vec_dec<vector<T>> {
  static constexpr int dim = vec_dec<T>::dim + 1;
  using type = typename vec_dec<T>::type;
};
static_assert(is_same<typename vec_dec<vec_t<3, ll>>::type, ll>::value, "");
static_assert(vec_dec<vec_t<3, ll>>::dim == 3, "");

template <typename T = ll> vector<T> makev(size_t a) { return vector<T>(a); }

template <typename T = ll, typename... Ts> auto makev(size_t a, Ts... ts) {
  return vector<decltype(makev<T>(ts...))>(a, makev<T>(ts...));
} // ex:  auto dp =  makev<ll>(4,5) => vector<vector<ll>> dp(4,vector<ll>(5));

template <typename T>
struct is_vector : std::false_type {}; // check if T is vector

template <typename T> struct is_vector<vector<T>> : std::true_type {};
static_assert(is_vector<vector<ll>>::value == true &&
                  is_vector<ll>::value == false,
              "");

// check if T is vector
template <typename T> struct is_pair : std::false_type {};

template <typename T, typename S>
struct is_pair<pair<T, S>> : std::true_type {};
static_assert(is_pair<pll>::value == true && is_pair<ll>::value == false, "");

template <typename T, typename V,
          typename enable_if<!is_vector<T>::value, nullptr_t>::type = nullptr>
void fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V,
          typename enable_if<is_vector<T>::value, nullptr_t>::type = nullptr>
void fill_v(T &t, const V &v) {
  for (auto &&x : t)
    fill_v(x, v);
} // ex:  fill_v(dp, INF);

namespace std {
template <class T> bool operator<(const complex<T> &a, const complex<T> &b) {
  return a.real() == b.real() ? a.imag() < b.imag() : a.real() < b.real();
}
}; // namespace std

template <typename T, typename S>
istream &operator>>(istream &istr, pair<T, S> &x) {
  return istr >> x.first >> x.second;
}
template <typename T> istream &operator>>(istream &istr, vector<T> &x) {
  rep(i, 0, x.size()) istr >> x[i];
  return istr;
}
template <typename T> istream &operator>>(istream &istr, complex<T> &x) {
  T r, i;
  istr >> r >> i;
  x.real(r);
  x.imag(i);
  return istr;
}

template <typename T, typename Delim_t = string,
          typename enable_if<!is_vector<T>::value, nullptr_t>::type = nullptr>
void write(T &x, Delim_t delim = " ") {
  cout << x << delim;
}
template <typename T, typename Delim_t = string,
          typename enable_if<is_vector<T>::value, nullptr_t>::type = nullptr>
void write(T &x, Delim_t delim = " ") {
  rep(i, 0, x.size()) write(x[i], (i == (x.size() - 1) ? "" : delim));
  cout << '\\n';
}

template <typename T> void chmin(T &a, T b) {
  if (a > b)
    a = b;
}
template <typename T> void chmax(T &a, T b) {
  if (a < b)
    a = b;
}

vll seq(ll i, ll j) {
  vll res(j - i);
  rep(k, i, j) res[k] = i + k;
  return res;
}

constexpr ll POW_0(ll x, ll y) {
  if (y == 0)
    return 1;
  if (y == 1)
    return x;
  if (y == 2)
    return x * x;
  if (y % 2 == 0)
    return POW_0(POW_0(x, y / 2), 2LL);
  return ((POW_0(POW_0(x, y / 2), 2LL)) * (x));
}

constexpr ll POW(ll x, ll y, ll mod = 0) {
  if (mod == 0)
    return POW_0(x, y);
  if (y == 0)
    return 1;
  if (y == 1)
    return x % mod;
  if (y == 2)
    return x * x % mod;
  if (y % 2 == 0)
    return POW(POW(x, y / 2, mod), 2LL, mod) % mod;
  return ((POW(POW(x, y / 2, mod), 2LL, mod)) * (x % mod)) % mod;
}

template <typename Inputs, typename Functor,
          typename T = typename Inputs::value_type>
void sort_by(Inputs &inputs, Functor f) {
  std::sort(std::begin(inputs), std::end(inputs),
            [&f](const T &lhs, const T &rhs) { return f(lhs) < f(rhs); });
}

template <typename Inputs, typename Functor,
          typename T = typename Inputs::value_type>
void stable_sort_by(Inputs &inputs, Functor f) {
  std::stable_sort(
      std::begin(inputs), std::end(inputs),
      [&f](const T &lhs, const T &rhs) { return f(lhs) < f(rhs); });
}

template <typename Inputs> void sort_uniq(Inputs &inputs) {
  sort(all(inputs));
  inputs.erase(unique(all(inputs)), inputs.end());
}

vector<string> split(const string &s, char delim) {
  vector<string> elems;
  stringstream ss(s);
  string item;
  if (s.size() > 0 && s.front() == delim) {
    elems.push_back("");
  }
  while (getline(ss, item, delim)) {
    if (!item.empty()) {
      elems.push_back(item);
    }
  }
  if (s.size() > 0 && s.back() == delim) {
    elems.push_back("");
  }
  return elems;
}

template <class T> map<T, ll> inv_map(vector<T> &x) {
  map<T, ll> res;
  rep(i, 0, x.size()) { res[x[i]] = i; }
  return res;
}
template <class T, class val_t = typename T::value_type,
          enable_if_t<!is_same<T, set<val_t>>::value> * = nullptr>
constexpr bool exist(const T &container, val_t val) {
  return find(all(container), val) != container.end();
}
template <class T, class val_t = typename T::value_type,
          enable_if_t<is_same<T, set<val_t>>::value> * = nullptr>
constexpr bool exist(const T &container, val_t val) {
  return container.find(val) != container.end();
}

// inner prod: |a||b|cos(theta)
template <class T> T dot(complex<T> a, complex<T> b) {
  return a.real() * b.real() + a.imag() * b.imag();
}
// outer prod |a||b|sin(theta)
template <class T> T cross(complex<T> a, complex<T> b) {
  return a.real() * b.imag() - a.imag() * b.real();
}

ll div_ferm(ll val, ll b, ll mod) { return (val * POW(b, mod - 2, mod)) % mod; }

// === Modint ===
// static uint_fast64_t runtime_modulus = MOD;

template <ll modulus = MOD> class modint {
public:
  ll val;
  constexpr modint() : val(0) {}
  constexpr modint(ll x) : val((x %= mod()) < 0 ? x + mod() : x) {}
  constexpr modint(ll x, ll modulus_) {
    set_modulo(modulus_);
    val = (x %= mod()) < 0 ? x + mod() : x;
  }
  template <class Ret = ll &>
  static auto modulo() -> std::enable_if_t<(modulus <= 0), Ret> {
    static ll runtime_modulus = numeric_limits<ll>::max();
    return runtime_modulus; // singleton technique
  }
  template <class Ret = const ll>
  static auto mod() -> std::enable_if_t<(modulus <= 0), Ret> {
    return modulo();
  }

  template <class Ret = const ll>
  static constexpr auto mod() -> std::enable_if_t<(modulus > 0), Ret> {
    return modulus;
  }

  template <ll modulus_ = modulus,
            enable_if_t<(modulus_ <= 0), nullptr_t> = nullptr>
  static void set_modulo(ll mod) {
    modulo() = mod;
  }
  void reset_modulo(ll modulus_) {
    modulo() = modulus_;
    val %= mod();
  }
  constexpr modint inv() { return pow(mod() - 2); }
  constexpr ll value() const noexcept { return val; }
  constexpr modint operator+(const modint rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint operator-(const modint rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint operator*(const modint rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint operator/(const modint rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  modint &operator+=(const modint rhs) noexcept {
    val += rhs.val;
    if (val >= mod()) {
      val -= mod();
    }
    return *this;
  }
  modint &operator-=(const modint rhs) noexcept {
    if (val < rhs.val) {
      val += mod();
    }
    val -= rhs.val;
    return *this;
  }
  modint &operator*=(const modint rhs) noexcept {
    val = val * rhs.val % mod();
    return *this;
  }
  modint &operator/=(modint rhs) noexcept {
    ll exp = mod() - 2;
    while (exp) {
      if (exp % 2) {
        *this *= rhs;
      }
      rhs *= rhs;
      exp /= 2;
    }
    return *this;
  }
  modint &operator++() noexcept { return *this += modint(1); }
  modint operator++(int) noexcept {
    modint t = *this;
    *this += modint(1);
    return t;
  }
  modint &operator--() noexcept { return *this -= modint(1); }
  modint operator--(int) noexcept {
    modint t = *this;
    *this -= modint(1);
    return t;
  }
  constexpr modint operator-() { return val ? mod() - val : val; }
  constexpr bool operator==(const modint rhs) const noexcept {
    return val == rhs.value();
  }
  constexpr bool operator!=(const modint rhs) const noexcept {
    return val != rhs.value();
  }
  constexpr bool operator<(const modint rhs) const noexcept {
    return val < rhs.value();
  }
  static constexpr modint zero() { return modint(0); }
  static constexpr modint unit() { return modint(1); }

  modint pow(long long k) const {
    modint v = *this;
    modint res(1), tmp(v);
    while (k) {
      if (k & 1)
        res *= tmp;
      tmp *= tmp;
      k >>= 1;
    }
    return res;
  }

  ll log(modint b) {
    modint val = *this;
    const ll sq = 40000;
    map<modint, ll> dp;
    // dp.reserve(sq);
    modint res(1);
    for (ll r = 0; r < sq; r++) {
      if (!dp.count(res))
        dp[res] = r;
      res *= val;
    }
    modint p = val.inv().pow(sq);
    res = b;
    for (ll q = 0; q <= mod() / sq + 1; q++) {
      if (dp.count(res)) {
        ll idx = q * sq + dp[res];
        if (idx > 0)
          return idx;
      }
      res *= p;
    }
    return INF;
  }
  friend ostream &operator<<(ostream &o, const modint<modulus> &t) {
    o << t.value();
    return o;
  }
  friend istream &operator>>(istream &in, modint<modulus> &t) {
    ll x;
    in >> x;
    t = modint<modulus>(x);
    return in;
  }
  friend modint<modulus> POW(modint<modulus> x, ll n) {
    return modint<modulus>(POW(x.value(), n, mod()));
  }
};
// user defined literal
modint<MOD> operator"" _mod(unsigned long long x) { return modint<MOD>(x); }

class Combination {
  // this calculates combination (nCk).
  // Constructor runs in O(MAX).
  // get(n,k) returns nCk in O(1).

  ll mod, N_MAX;
  vll fac;
  vll finv;
  vll inv;

public:
  Combination(ll mod = MOD, ll N_MAX = 210000)
      : mod(mod), N_MAX(max(N_MAX, (ll)2)), fac(vll(N_MAX + 1)),
        finv(vll(N_MAX + 1)), inv(vll(N_MAX + 1)) {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    pre_process(2LL, N_MAX + 1);
  }

  ll operator()(ll n, ll k) {
    // choose k from n
    if (N_MAX < n)
      pre_process(N_MAX + 1, n + 1);

    if (0 <= n && n < k)
      return 0;
    if (k == 0)
      return 1;
    if (n < 0)
      return operator()(-n + k - 1, k) * (k % 2 ? -1 : 0);
    return fac[n] * (finv[k] * finv[n - k] % mod) % mod;
  }
  ll H(ll n, ll k) {
    // 1) 区間[0, k) を（空を許して）n個に分割する場合の数
    // 2) n個の中からk個を重複を許して選ぶ
    return operator()(n + k - 1, k);
  }
  ll P(ll n, ll k) {
    // n (n-1) ... (n-k+1)
    return (n < k || n < 0) ? 0 : fac[n] * finv[n - k];
  }
  ll Fac(ll n) { return P(n, n); }
  ll FacInv(ll n) { return n < 0 ? 0 : finv[n]; }

private:
  void pre_process(ll m, ll n) {
    if (N_MAX < n) {
      fac.resize(n);
      inv.resize(n);
      finv.resize(n);
    }
    rep(i, m, n) {
      fac[i] = fac[i - 1] * i % mod;
      inv[i] = mod - inv[mod % i] * (mod / i) % mod;
      finv[i] = finv[i - 1] * inv[i] % mod;
    }
  }
};

ll choose(int n, int r) { // O(r) for small n
  ll acc = 1;
  rep(i, 0, r) acc = acc * (n - i) / (i + 1);
  return acc;
}

ll gcd(ll val, ll b) {
  if (val % b == 0)
    return b;
  else
    return gcd(b, val % b);
}

vll divisor(ll n) {
  // returns common divisors in O(sqrt(min(n,m)))
  vll res;
  for (ll i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      res.push_back(i);
      res.push_back(n / i);
    }
    if (i * i == n)
      res.push_back(i);
  }
  sort(res.begin(), res.end());
  return res;
}

vll divisor(ll n, ll m) {
  // returns common divisors in O(sqrt(min(n,m)))
  if (n > m)
    swap(n, m);
  vll res;
  for (ll i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      if (m % i == 0)
        res.push_back(i);
      if (m % (n / i) == 0)
        res.push_back(n / i);
    }
    if (i * i == n && m % i == 0)
      res.push_back(i);
  }
  sort(res.begin(), res.end());
  return res;
}

vpll prime_factorize(ll n) {
  // returns prime factorization of n in O(sprt(n))
  vector<pll> res;
  for (ll p = 2; p * p <= n; ++p) {
    if (n % p != 0)
      continue;
    ll num = 0;
    while (n % p == 0) {
      ++num;
      n /= p;
    }
    res.push_back({p, num});
  }
  if (n != 1)
    res.push_back(make_pair(n, 1));
  return res;
}

int main() {

  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(12);

  ll n, k;
  cin >> n >> k;
  modint<> res = 0;
  vector<modint<>> cnt(n + 1);
  rrep(i, 1, k + 1) {
    cnt[i] = POW(modint<>(k / i), n);
    rep(j, 2, k / i + 1) cnt[i] -= cnt[i * j];
  }
  rep(i, 1, k + 1) { res += cnt[i] * i; }
  cout << res << endl;
  return 0;
}