#913653 (C++17) No.1049 Zero (Exhaust)

• 問題: No.1049 Zero (Exhaust)
• ユーザー: kuhaku
• 提出日時: 2023-09-17 13:56:45
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 11 ms / 2,000 ms
• コード長: 23,101 bytes
• コンパイル時間: 3,333 ms
• コンパイル使用メモリ: 219,120 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-07-04 09:21:06
• 合計ジャッジ時間: 4,031 ms
• ジャッジサーバーID （参考情報）: judge1 / judge3

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	8 ms; 5,376 KB
testcase_04	AC	1 ms; 5,376 KB
testcase_05	AC	7 ms; 5,376 KB
testcase_06	AC	11 ms; 5,376 KB
testcase_07	AC	3 ms; 5,376 KB
testcase_08	AC	4 ms; 5,376 KB
testcase_09	AC	8 ms; 5,376 KB
testcase_10	AC	8 ms; 5,376 KB
testcase_11	AC	8 ms; 5,376 KB
testcase_12	AC	9 ms; 5,376 KB
testcase_13	AC	4 ms; 5,376 KB
testcase_14	AC	6 ms; 5,376 KB
testcase_15	AC	7 ms; 5,376 KB
testcase_16	AC	7 ms; 5,376 KB
testcase_17	AC	7 ms; 5,376 KB
testcase_18	AC	9 ms; 5,376 KB
testcase_19	AC	8 ms; 5,376 KB
testcase_20	AC	4 ms; 5,376 KB
testcase_21	AC	8 ms; 5,376 KB
testcase_22	AC	5 ms; 5,376 KB
testcase_23	AC	10 ms; 5,376 KB
testcase_24	AC	10 ms; 5,376 KB

ソースコード

#line 1 "a.cpp"
#define PROBLEM ""
#line 2 "/home/kuhaku/atcoder/github/algo/lib/template/template.hpp"
#pragma GCC target("sse4.2,avx2,bmi2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
template <class T, class U>
bool chmax(T &a, const U &b) {
    return a < (T)b ? a = (T)b, true : false;
}
template <class T, class U>
bool chmin(T &a, const U &b) {
    return (T)b < a ? a = (T)b, true : false;
}
constexpr std::int64_t INF = 1000000000000000003;
constexpr int Inf = 1000000003;
constexpr int MOD = 1000000007;
constexpr int MOD_N = 998244353;
constexpr double EPS = 1e-7;
constexpr double PI = M_PI;
#line 3 "/home/kuhaku/atcoder/github/algo/lib/internal/internal_math.hpp"

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr std::int64_t safe_mod(std::int64_t x, std::int64_t m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
    unsigned int _m;
    std::uint64_t im;

    // @param m `1 <= m`
    explicit barrett(unsigned int m) : _m(m), im((std::uint64_t)(-1) / m + 1) {}

    // @return m
    unsigned int umod() const { return _m; }

    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    unsigned int mul(unsigned int a, unsigned int b) const {
        std::uint64_t z = a;
        z *= b;
        std::uint64_t x = (std::uint64_t)(((__uint128_t)(z)*im) >> 64);
        std::uint64_t y = x * _m;
        return (unsigned int)(z - y + (z < y ? _m : 0));
    }
};

struct montgomery {
    std::uint64_t _m;
    std::uint64_t im;
    std::uint64_t r2;

    // @param m `1 <= m`
    explicit constexpr montgomery(std::uint64_t m) : _m(m), im(m), r2(-__uint128_t(m) % m) {
        for (int i = 0; i < 5; ++i) im = im * (2 - _m * im);
        im = -im;
    }

    // @return m
    constexpr std::uint64_t umod() const { return _m; }

    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    constexpr std::uint64_t mul(std::uint64_t a, std::uint64_t b) const { return mr(mr(a, b), r2); }

    constexpr std::uint64_t exp(std::uint64_t a, std::uint64_t b) const {
        std::uint64_t res = 1, p = mr(a, r2);
        while (b) {
            if (b & 1) res = mr(res, p);
            p = mr(p, p);
            b >>= 1;
        }
        return res;
    }

    constexpr bool same_pow(std::uint64_t x, int s, std::uint64_t n) const {
        x = mr(x, r2), n = mr(n, r2);
        for (int r = 0; r < s; r++) {
            if (x == n) return true;
            x = mr(x, x);
        }
        return false;
    }

  private:
    constexpr std::uint64_t mr(std::uint64_t x) const {
        return ((__uint128_t)(x * im) * _m + x) >> 64;
    }
    constexpr std::uint64_t mr(std::uint64_t a, std::uint64_t b) const {
        __uint128_t t = (__uint128_t)a * b;
        std::uint64_t inc = std::uint64_t(t) != 0;
        std::uint64_t x = t >> 64, y = ((__uint128_t)(a * b * im) * _m) >> 64;
        unsigned long long z = 0;
        bool f = __builtin_uaddll_overflow(x, y, &z);
        z += inc;
        return f ? z - _m : z;
    }
};

constexpr bool is_SPRP32(std::uint32_t n, std::uint32_t a) {
    std::uint32_t d = n - 1, s = 0;
    while ((d & 1) == 0) ++s, d >>= 1;
    std::uint64_t cur = 1, pw = d;
    while (pw) {
        if (pw & 1) cur = (cur * a) % n;
        a = (std::uint64_t)a * a % n;
        pw >>= 1;
    }
    if (cur == 1) return true;
    for (std::uint32_t r = 0; r < s; r++) {
        if (cur == n - 1) return true;
        cur = cur * cur % n;
    }
    return false;
}

// given 2 <= n,a < 2^64, a prime, check whether n is a-SPRP
constexpr bool is_SPRP64(const montgomery &m, std::uint64_t a) {
    auto n = m.umod();
    if (n == a) return true;
    if (n % a == 0) return false;
    std::uint64_t d = n - 1;
    int s = 0;
    while ((d & 1) == 0) ++s, d >>= 1;
    std::uint64_t cur = m.exp(a, d);
    if (cur == 1) return true;
    return m.same_pow(cur, s, n - 1);
}

constexpr bool is_prime_constexpr(std::uint64_t x) {
    if (x == 2 || x == 3 || x == 5 || x == 7) return true;
    if (x % 2 == 0 || x % 3 == 0 || x % 5 == 0 || x % 7 == 0) return false;
    if (x < 121) return (x > 1);
    montgomery m(x);
    constexpr std::uint64_t bases[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
    for (auto a : bases) {
        if (!is_SPRP64(m, a)) return false;
    }
    return true;
}

constexpr bool is_prime_constexpr(std::int64_t x) {
    if (x < 0) return false;
    return is_prime_constexpr(std::uint64_t(x));
}

constexpr bool is_prime_constexpr(std::uint32_t x) {
    if (x == 2 || x == 3 || x == 5 || x == 7) return true;
    if (x % 2 == 0 || x % 3 == 0 || x % 5 == 0 || x % 7 == 0) return false;
    if (x < 121) return (x > 1);
    std::uint64_t h = x;
    h = ((h >> 16) ^ h) * 0x45d9f3b;
    h = ((h >> 16) ^ h) * 0x45d9f3b;
    h = ((h >> 16) ^ h) & 255;
    constexpr uint16_t bases[] = {
        15591, 2018,  166,   7429,  8064,  16045, 10503, 4399,  1949,  1295,  2776,  3620,  560,
        3128,  5212,  2657,  2300,  2021,  4652,  1471,  9336,  4018,  2398,  20462, 10277, 8028,
        2213,  6219,  620,   3763,  4852,  5012,  3185,  1333,  6227,  5298,  1074,  2391,  5113,
        7061,  803,   1269,  3875,  422,   751,   580,   4729,  10239, 746,   2951,  556,   2206,
        3778,  481,   1522,  3476,  481,   2487,  3266,  5633,  488,   3373,  6441,  3344,  17,
        15105, 1490,  4154,  2036,  1882,  1813,  467,   3307,  14042, 6371,  658,   1005,  903,
        737,   1887,  7447,  1888,  2848,  1784,  7559,  3400,  951,   13969, 4304,  177,   41,
        19875, 3110,  13221, 8726,  571,   7043,  6943,  1199,  352,   6435,  165,   1169,  3315,
        978,   233,   3003,  2562,  2994,  10587, 10030, 2377,  1902,  5354,  4447,  1555,  263,
        27027, 2283,  305,   669,   1912,  601,   6186,  429,   1930,  14873, 1784,  1661,  524,
        3577,  236,   2360,  6146,  2850,  55637, 1753,  4178,  8466,  222,   2579,  2743,  2031,
        2226,  2276,  374,   2132,  813,   23788, 1610,  4422,  5159,  1725,  3597,  3366,  14336,
        579,   165,   1375,  10018, 12616, 9816,  1371,  536,   1867,  10864, 857,   2206,  5788,
        434,   8085,  17618, 727,   3639,  1595,  4944,  2129,  2029,  8195,  8344,  6232,  9183,
        8126,  1870,  3296,  7455,  8947,  25017, 541,   19115, 368,   566,   5674,  411,   522,
        1027,  8215,  2050,  6544,  10049, 614,   774,   2333,  3007,  35201, 4706,  1152,  1785,
        1028,  1540,  3743,  493,   4474,  2521,  26845, 8354,  864,   18915, 5465,  2447,  42,
        4511,  1660,  166,   1249,  6259,  2553,  304,   272,   7286,  73,    6554,  899,   2816,
        5197,  13330, 7054,  2818,  3199,  811,   922,   350,   7514,  4452,  3449,  2663,  4708,
        418,   1621,  1171,  3471,  88,    11345, 412,   1559,  194};
    return is_SPRP32(x, bases[h]);
}

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr std::int64_t pow_mod_constexpr(std::int64_t x, std::int64_t n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    std::uint64_t r = 1;
    std::uint64_t y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    std::int64_t d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr std::int64_t bases[3] = {2, 7, 61};
    for (std::int64_t a : bases) {
        std::int64_t t = d;
        std::int64_t y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n>
constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<std::int64_t, std::int64_t> inv_gcd(std::int64_t a, std::int64_t b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};
    std::int64_t s = b, t = a;
    std::int64_t m0 = 0, m1 = 1;
    while (t) {
        std::int64_t u = s / t;
        s -= t * u;
        m0 -= m1 * u;
        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (std::int64_t)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m>
constexpr int primitive_root = primitive_root_constexpr(m);

// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
std::uint64_t floor_sum_unsigned(std::uint64_t n, std::uint64_t m, std::uint64_t a,
                                 std::uint64_t b) {
    std::uint64_t ans = 0;
    while (true) {
        if (a >= m) {
            ans += n * (n - 1) / 2 * (a / m);
            a %= m;
        }
        if (b >= m) {
            ans += n * (b / m);
            b %= m;
        }

        std::uint64_t y_max = a * n + b;
        if (y_max < m) break;
        // y_max < m * (n + 1)
        // floor(y_max / m) <= n
        n = (std::uint64_t)(y_max / m);
        b = (std::uint64_t)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

}  // namespace internal
#line 3 "/home/kuhaku/atcoder/github/algo/lib/internal/internal_type_traits.hpp"

namespace internal {

template <class T>
using is_signed_int128 = typename std::conditional<std::is_same<T, __int128_t>::value ||
                                                       std::is_same<T, __int128>::value,
                                                   std::true_type, std::false_type>::type;

template <class T>
using is_unsigned_int128 = typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                                         std::is_same<T, unsigned __int128>::value,
                                                     std::true_type, std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t, unsigned __int128>;

template <class T>
using is_integral =
    typename std::conditional<std::is_integral<T>::value || is_signed_int128<T>::value ||
                                  is_unsigned_int128<T>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using is_signed_int =
    typename std::conditional<(is_integral<T>::value && std::is_signed<T>::value) ||
                                  is_signed_int128<T>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value && std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value, make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T>
using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal
#line 5 "/home/kuhaku/atcoder/github/algo/lib/math/modint.hpp"

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T>
using is_modint = std::is_base_of<modint_base, T>;
template <class T>
using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)> * = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static constexpr mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    constexpr static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T> * = nullptr>
    constexpr static_modint(T v) : _v(0) {
        std::int64_t x = (std::int64_t)(v % (std::int64_t)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T> * = nullptr>
    constexpr static_modint(T v) : _v(0) {
        _v = (unsigned int)(v % umod());
    }

    constexpr unsigned int val() const { return _v; }

    constexpr mint &operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    constexpr mint &operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    constexpr mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    constexpr mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    constexpr mint &operator+=(const mint &rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    constexpr mint &operator-=(const mint &rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    constexpr mint &operator*=(const mint &rhs) {
        std::uint64_t z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    constexpr mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }

    constexpr mint operator+() const { return *this; }
    constexpr mint operator-() const { return mint() - *this; }

    constexpr mint pow(std::int64_t n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    constexpr mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }

    friend constexpr mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
    friend constexpr mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
    friend constexpr mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
    friend constexpr mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
    friend constexpr bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
    friend constexpr bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }
    friend std::istream &operator>>(std::istream &is, mint &rhs) {
        std::int64_t t;
        is >> t;
        rhs = mint(t);
        return is;
    }
    friend constexpr std::ostream &operator<<(std::ostream &os, const mint &rhs) {
        return os << rhs._v;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};

template <int id>
struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;

  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T> * = nullptr>
    dynamic_modint(T v) {
        std::int64_t x = (std::int64_t)(v % (std::int64_t)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T> * = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }

    unsigned int val() const { return _v; }

    mint &operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint &operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint &operator+=(const mint &rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint &operator-=(const mint &rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint &operator*=(const mint &rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(std::int64_t n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }

    friend mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
    friend mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
    friend mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
    friend mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
    friend bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
    friend bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }
    friend std::istream &operator>>(std::istream &is, mint &rhs) {
        std::int64_t t;
        is >> t;
        rhs = mint(t);
        return is;
    }
    friend constexpr std::ostream &operator<<(std::ostream &os, const mint &rhs) {
        return os << rhs._v;
    }

  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id>
internal::barrett dynamic_modint<id>::bt(998244353);

using modint998 = static_modint<998244353>;
using modint107 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class>
struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

}  // namespace internal
#line 3 "/home/kuhaku/atcoder/github/algo/lib/template/macro.hpp"
#define FOR(i, m, n) for (int i = (m); i < int(n); ++i)
#define FORR(i, m, n) for (int i = (m)-1; i >= int(n); --i)
#define FORL(i, m, n) for (int64_t i = (m); i < int64_t(n); ++i)
#define rep(i, n) FOR (i, 0, n)
#define repn(i, n) FOR (i, 1, n + 1)
#define repr(i, n) FORR (i, n, 0)
#define repnr(i, n) FORR (i, n + 1, 1)
#define all(s) (s).begin(), (s).end()
#line 3 "/home/kuhaku/atcoder/github/algo/lib/template/sonic.hpp"
struct Sonic {
    Sonic() {
        std::ios::sync_with_stdio(false);
        std::cin.tie(nullptr);
    }

    constexpr void operator()() const {}
} sonic;
#line 5 "/home/kuhaku/atcoder/github/algo/lib/template/atcoder.hpp"
using namespace std;
using ll = std::int64_t;
using ld = long double;
template <class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
    return is >> p.first >> p.second;
}
template <class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
    for (T &i : v) is >> i;
    return is;
}
template <class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
    return os << '(' << p.first << ',' << p.second << ')';
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
    for (auto it = v.begin(); it != v.end(); ++it) {
        os << (it == v.begin() ? "" : " ") << *it;
    }
    return os;
}
template <class Head, class... Tail>
void co(Head &&head, Tail &&...tail) {
    if constexpr (sizeof...(tail) == 0) std::cout << head << '\n';
    else std::cout << head << ' ', co(std::forward<Tail>(tail)...);
}
template <class Head, class... Tail>
void ce(Head &&head, Tail &&...tail) {
    if constexpr (sizeof...(tail) == 0) std::cerr << head << '\n';
    else std::cerr << head << ' ', ce(std::forward<Tail>(tail)...);
}
template <typename T, typename... Args>
auto make_vector(T x, int arg, Args... args) {
    if constexpr (sizeof...(args) == 0) return std::vector<T>(arg, x);
    else return std::vector(arg, make_vector<T>(x, args...));
}
void setp(int n) {
    std::cout << std::fixed << std::setprecision(n);
}
void Yes(bool is_correct = true) {
    std::cout << (is_correct ? "Yes" : "No") << '\n';
}
void No(bool is_not_correct = true) {
    Yes(!is_not_correct);
}
void YES(bool is_correct = true) {
    std::cout << (is_correct ? "YES" : "NO") << '\n';
}
void NO(bool is_not_correct = true) {
    YES(!is_not_correct);
}
void Takahashi(bool is_correct = true) {
    std::cout << (is_correct ? "Takahashi" : "Aoki") << '\n';
}
void Aoki(bool is_not_correct = true) {
    Takahashi(!is_not_correct);
}
#line 4 "a.cpp"

using Mint = modint107;

int main(void) {
    int p, k;
    cin >> p >> k;
    Mint a = 1, b = 0;
    rep (i, k) {
        Mint c = a + b + a * p + b;
        Mint d = (a + b) * (p - 1) + b * (p - 1);
        a = c, b = d;
    }
    co(a);

    return 0;
}