Problem: Find the number of sequences of N non-negative integers A_1, A_2, ..., A_N that satisfy the following conditions:

* L \leq A_1 + A_2 + ... + A_N \leq R
* When the N elements are sorted in non-increasing order, the M-th and (M+1)-th elements are equal.



Since the answer can be enormous, print it modulo 10^9+7.

Constraints

* All values in input are integers.
* 1 \leq M < N \leq 3 \times 10^5
* 1 \leq L \leq R \leq 3 \times 10^5

Input

Input is given from Standard Input in the following format:


N M L R


Output

Print the number of sequences of N non-negative integers, modulo 10^9+7.

Examples

Input

4 2 3 7


Output

105


Input

2 1 4 8


Output

3


Input

141592 6535 89793 238462


Output

933832916

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using Int = long long;  // clang-format off
#define REP_(i, a_, b_, a, b, ...) for (Int i = (a), lim##i = (b); i < lim##i; i++)
#define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define ALL(v) std::begin(v), std::end(v)
struct SetupIO { SetupIO() { std::cin.tie(nullptr), std::ios::sync_with_stdio(false), std::cout << std::fixed << std::setprecision(13); } } setup_io;
#ifndef dump
#define dump(...)
#endif  // clang-format on

/**
 *    author:  knshnb
 *    created: Sat Aug 29 02:12:00 JST 2020
 **/

template <class T> T pow(T x, long long n, const T UNION = 1) {
    T ret = UNION;
    while (n) {
        if (n & 1) ret *= x;
        x *= x;
        n >>= 1;
    }
    return ret;
}

/// @docs src/Math/ModInt.md
template <int Mod> struct ModInt {
    int x;
    static int runtime_mod;
    static std::unordered_map<int, int> to_inv;
    // テンプレート引数が負のときは実行時ModInt
    static int mod() { return Mod < 0 ? runtime_mod : Mod; }
    static void set_runtime_mod(int mod) {
        static_assert(Mod < 0, "template parameter Mod must be negative for runtime ModInt");
        runtime_mod = mod;
        to_inv.clear();
    }
    ModInt() : x(0) {}
    ModInt(long long x_) {
        if ((x = x_ % mod() + mod()) >= mod()) x -= mod();
    }

    ModInt& operator+=(ModInt rhs) {
        if ((x += rhs.x) >= mod()) x -= mod();
        return *this;
    }
    ModInt& operator*=(ModInt rhs) {
        x = (unsigned long long)x * rhs.x % mod();
        return *this;
    }
    ModInt& operator-=(ModInt rhs) {
        if ((x -= rhs.x) < 0) x += mod();
        return *this;
    }
    ModInt& operator/=(ModInt rhs) {
        x = (unsigned long long)x * rhs.inv().x % mod();
        return *this;
    }
    ModInt operator-() const { return -x < 0 ? mod() - x : -x; }
    ModInt operator+(ModInt rhs) const { return ModInt(*this) += rhs; }
    ModInt operator*(ModInt rhs) const { return ModInt(*this) *= rhs; }
    ModInt operator-(ModInt rhs) const { return ModInt(*this) -= rhs; }
    ModInt operator/(ModInt rhs) const { return ModInt(*this) /= rhs; }
    bool operator==(ModInt rhs) const { return x == rhs.x; }
    bool operator!=(ModInt rhs) const { return x != rhs.x; }
    ModInt inv() const { return to_inv.count(this->x) ? to_inv[this->x] : (to_inv[this->x] = pow(*this, mod() - 2).x); }

    friend std::ostream& operator<<(std::ostream& s, ModInt<Mod> a) {
        s << a.x;
        return s;
    }
    friend std::istream& operator>>(std::istream& s, ModInt<Mod>& a) {
        long long tmp;
        s >> tmp;
        a = ModInt<Mod>(tmp);
        return s;
    }
    friend std::string to_string(ModInt<Mod> a) { return std::to_string(a.x); }
};
template <int Mod> std::unordered_map<int, int> ModInt<Mod>::to_inv;
template <int Mod> int ModInt<Mod>::runtime_mod;

#ifndef CALL_FROM_TEST
using mint = ModInt<1000000007>;
#endif

template <class T> struct Combination {
    std::vector<T> fact, fact_inv;
    Combination(int n = 1000003) : fact(n + 1, 1), fact_inv(n + 1) {
        for (int i = 0; i < n; i++) fact[i + 1] = fact[i] * (i + 1);
        fact_inv[n] = (T)1 / fact[n];
        for (int i = n - 1; i >= 0; i--) fact_inv[i] = fact_inv[i + 1] * (i + 1);
        // for (int i = 0; i < n + 1; i++) assert(fact[i] * fact_inv[i] == 1);
    }
    T operator()(int n, int r) { return fact[n] * fact_inv[r] * fact_inv[n - r]; }
};

mint solve(Int n, Int m, Int R) {
    Combination<mint> comb;
    auto calc = [&](Int offset) {
        mint acc = 0;
        REP(k, R + 1) {
            REP(i, m + 1) {
                Int deg = i * (k + offset) + (k + 1) * (n - m);
                if (deg > R) break;
                mint val = comb(m, i) * (i % 2 ? -1 : 1);
                Int rem_deg = R - deg;
                acc += comb(n + rem_deg, rem_deg) * val;
            }
        }
        return acc;
    };

    mint all = 0;
    REP(x, R + 1) all += comb(x + n - 1, x);
    return all - comb(n, m) * (calc(1) - calc(0));
}

signed main() {
    Int n, m, L, R;
    std::cin >> n >> m >> L >> R;
    m = n - m;
    mint ans = solve(n, m, R) - solve(n, m, L - 1);
    std::cout << ans << std::endl;
}