#include <iostream>
#include <numeric>
#include <vector>

template <class T>
std::vector<T> vec(int len, T elem) { return std::vector<T>(len, elem); }

template <int MOD>
struct ModInt {
    using lint = long long;
    int val;

    // constructor
    ModInt(lint v = 0) : val(v % MOD) {
        if (val < 0) val += MOD;
    };

    // unary operator
    ModInt operator+() const { return ModInt(val); }
    ModInt operator-() const { return ModInt(MOD - val); }
    ModInt inv() const { return this->pow(MOD - 2); }

    // arithmetic
    ModInt operator+(const ModInt& x) const { return ModInt(*this) += x; }
    ModInt operator-(const ModInt& x) const { return ModInt(*this) -= x; }
    ModInt operator*(const ModInt& x) const { return ModInt(*this) *= x; }
    ModInt operator/(const ModInt& x) const { return ModInt(*this) /= x; }
    ModInt pow(lint n) const {
        auto x = ModInt(1);
        auto b = *this;
        while (n > 0) {
            if (n & 1) x *= b;
            n >>= 1;
            b *= b;
        }
        return x;
    }

    // compound assignment
    ModInt& operator+=(const ModInt& x) {
        if ((val += x.val) >= MOD) val -= MOD;
        return *this;
    }
    ModInt& operator-=(const ModInt& x) {
        if ((val -= x.val) < 0) val += MOD;
        return *this;
    }
    ModInt& operator*=(const ModInt& x) {
        val = lint(val) * x.val % MOD;
        return *this;
    }
    ModInt& operator/=(const ModInt& x) { return *this *= x.inv(); }

    // compare
    bool operator==(const ModInt& b) const { return val == b.val; }
    bool operator!=(const ModInt& b) const { return val != b.val; }

    // I/O
    friend std::istream& operator>>(std::istream& is, ModInt& x) noexcept { return is >> x.val; }
    friend std::ostream& operator<<(std::ostream& os, const ModInt& x) noexcept { return os << x.val; }
};

constexpr int MOD = 1e9 + 7;
using mint = ModInt<MOD>;

void solve() {
    int n, k;
    std::cin >> n >> k;

    const int X = n * (n + 1) / 2;
    std::vector<mint> dp(X + 1, 0), pat(X + 1, 0);
    pat[0] = 1;

    auto ndp = dp, npat = pat;
    for (int i = n; i >= 1; --i) {
        std::fill(ndp.begin(), ndp.end(), 0);
        std::fill(npat.begin(), npat.end(), 0);

        for (int c = 0; c <= X; ++c) {
            for (int a = 0; a <= k; ++a) {
                int nc = (a > i ? 0 : (a + c) / i);
                if (c + nc > X) continue;

                ndp[c + nc] += dp[c] + pat[c] * (a - nc);
                npat[c + nc] += pat[c];
            }
        }

        std::swap(dp, ndp);
        std::swap(pat, npat);
    }

    std::cout << std::accumulate(dp.begin(), dp.end(), mint(0)) << std::endl;
}

int main() {
    std::cin.tie(nullptr);
    std::cout.tie(nullptr);
    std::ios::sync_with_stdio(false);

    solve();

    return 0;
}

### Prompt

Please create a solution in Cpp to the following problem:

Consider the following game:

* The game is played using a row of N squares and many stones.
* First, a_i stones are put in Square i\ (1 \leq i \leq N).
* A player can perform the following operation as many time as desired: "Select an integer i such that Square i contains exactly i stones. Remove all the stones from Square i, and add one stone to each of the i-1 squares from Square 1 to Square i-1."
* The final score of the player is the total number of the stones remaining in the squares.



For a sequence a of length N, let f(a) be the minimum score that can be obtained when the game is played on a.

Find the sum of f(a) over all sequences a of length N where each element is between 0 and K (inclusive). Since it can be extremely large, find the answer modulo 1000000007 (= 10^9+7).

Constraints

* 1 \leq N \leq 100
* 1 \leq K \leq N

Input

Input is given from Standard Input in the following format:


N K


Output

Print the sum of f(a) modulo 1000000007 (= 10^9+7).

Examples

Input

2 2


Output

10


Input

20 17


Output

983853488

### Response

```cpp
#include <iostream>
#include <numeric>
#include <vector>

template <class T>
std::vector<T> vec(int len, T elem) { return std::vector<T>(len, elem); }

template <int MOD>
struct ModInt {
    using lint = long long;
    int val;

    // constructor
    ModInt(lint v = 0) : val(v % MOD) {
        if (val < 0) val += MOD;
    };

    // unary operator
    ModInt operator+() const { return ModInt(val); }
    ModInt operator-() const { return ModInt(MOD - val); }
    ModInt inv() const { return this->pow(MOD - 2); }

    // arithmetic
    ModInt operator+(const ModInt& x) const { return ModInt(*this) += x; }
    ModInt operator-(const ModInt& x) const { return ModInt(*this) -= x; }
    ModInt operator*(const ModInt& x) const { return ModInt(*this) *= x; }
    ModInt operator/(const ModInt& x) const { return ModInt(*this) /= x; }
    ModInt pow(lint n) const {
        auto x = ModInt(1);
        auto b = *this;
        while (n > 0) {
            if (n & 1) x *= b;
            n >>= 1;
            b *= b;
        }
        return x;
    }

    // compound assignment
    ModInt& operator+=(const ModInt& x) {
        if ((val += x.val) >= MOD) val -= MOD;
        return *this;
    }
    ModInt& operator-=(const ModInt& x) {
        if ((val -= x.val) < 0) val += MOD;
        return *this;
    }
    ModInt& operator*=(const ModInt& x) {
        val = lint(val) * x.val % MOD;
        return *this;
    }
    ModInt& operator/=(const ModInt& x) { return *this *= x.inv(); }

    // compare
    bool operator==(const ModInt& b) const { return val == b.val; }
    bool operator!=(const ModInt& b) const { return val != b.val; }

    // I/O
    friend std::istream& operator>>(std::istream& is, ModInt& x) noexcept { return is >> x.val; }
    friend std::ostream& operator<<(std::ostream& os, const ModInt& x) noexcept { return os << x.val; }
};

constexpr int MOD = 1e9 + 7;
using mint = ModInt<MOD>;

void solve() {
    int n, k;
    std::cin >> n >> k;

    const int X = n * (n + 1) / 2;
    std::vector<mint> dp(X + 1, 0), pat(X + 1, 0);
    pat[0] = 1;

    auto ndp = dp, npat = pat;
    for (int i = n; i >= 1; --i) {
        std::fill(ndp.begin(), ndp.end(), 0);
        std::fill(npat.begin(), npat.end(), 0);

        for (int c = 0; c <= X; ++c) {
            for (int a = 0; a <= k; ++a) {
                int nc = (a > i ? 0 : (a + c) / i);
                if (c + nc > X) continue;

                ndp[c + nc] += dp[c] + pat[c] * (a - nc);
                npat[c + nc] += pat[c];
            }
        }

        std::swap(dp, ndp);
        std::swap(pat, npat);
    }

    std::cout << std::accumulate(dp.begin(), dp.end(), mint(0)) << std::endl;
}

int main() {
    std::cin.tie(nullptr);
    std::cout.tie(nullptr);
    std::ios::sync_with_stdio(false);

    solve();

    return 0;
}

```