Problem:
Score : 600 points

Problem Statement

Snuke is standing on a two-dimensional plane. In one operation, he can move by 1 in the positive x-direction, or move by 1 in the positive y-direction.

Let us define a function f(r, c) as follows:

f(r,c) := (The number of paths from the point (0, 0) to the point (r, c) that Snuke can trace by repeating the operation above)

Given are integers r_1, r_2, c_1, and c_2.
Find the sum of f(i, j) over all pair of integers (i, j) such that r_1 ≤ i ≤ r_2 and c_1 ≤ j ≤ c_2, and compute this value modulo (10^9+7).

Constraints

1 ≤ r_1 ≤ r_2 ≤ 10^6

1 ≤ c_1 ≤ c_2 ≤ 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

r_1 c_1 r_2 c_2

Output

Print the sum of f(i, j) modulo (10^9+7).

Sample Input 1

1 1 2 2

Sample Output 1

14

For example, there are two paths from the point (0, 0) to the point (1, 1): (0,0) → (0,1) → (1,1) and (0,0) → (1,0) → (1,1), so f(1,1)=2.

Similarly, f(1,2)=3, f(2,1)=3, and f(2,2)=6. Thus, the sum is 14.

Sample Input 2

314 159 2653 589

Sample Output 2

602215194

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include "bits/stdc++.h"
// Begin Header {{{
#define all(x)          (x).begin(), (x).end()
#define rep(i, n)       for (i64 i = 0, i##_limit = (n); i < i##_limit; ++i)
#define reps(i, s, t)   for (i64 i = (s), i##_limit = (t); i <= i##_limit; ++i)
#define repr(i, s, t)   for (i64 i = (s), i##_limit = (t); i >= i##_limit; --i)
#ifndef DBG
#define trace(...)
#endif
using namespace std;
using i64 = int_fast64_t;
using pii = pair<i64, i64>;
template <class T, class U> inline bool chmax(T &a, const U &b) { return b > a && (a = b, true); }
template <class T, class U> inline bool chmin(T &a, const U &b) { return b < a && (a = b, true); }
constexpr int INF  = 0x3f3f3f3f;
constexpr i64 LINF = 0x3f3f3f3f3f3f3f3fLL;

template <class T>
inline vector<T> make_v(const T &initValue, size_t sz) {
    return vector<T>(sz, initValue);
}

template <class T, class... Args>
inline auto make_v(const T &initValue, size_t sz, Args... args) {
    return vector<decltype(make_v<T>(initValue, args...))>(sz, make_v<T>(initValue, args...));
}

inline void read() {}

template <class Head, class... Tail>
inline void read(Head &head, Tail&... tail) { cin >> head; read(tail...); }

inline void print() { cout << "\n"; }

template <class Head, class... Tail>
inline void print(Head &&head, Tail&&... tail) {
    cout << head;
    if (sizeof...(tail)) cout << ' ';
    print(forward<Tail>(tail)...);
}

template <class T>
inline ostream& operator<< (ostream &out, const vector<T> &vec) {
    static constexpr const char *delim[] = { " ", "" };
    for (const auto &e : vec) out << e << delim[&e == &vec.back()];
    return out;
}
// }}} End Header

constexpr int MOD = int(1e9) + 7;

// ModInt {{{
template<int64_t MOD>
class ModInt {
    int64_t value;
public:
    // constructor
    inline ModInt(int64_t val = 0) noexcept :
        value((val >= MOD) ? (val % MOD) : (val < 0) ? ((val + MOD) % MOD) : val) {}

    // プリミティブ整数型へのキャスト (型の明示:必要)
    template<class Int>
        explicit inline operator Int() const noexcept { return static_cast<Int>(value); }

    inline ModInt inv() const noexcept {
        return ModInt<MOD>::pow(value, MOD-2);
    }

    inline ModInt& operator+=(ModInt x) noexcept {
        if ((value += x.value) >= MOD) value -= MOD;
        return *this;
    }
    inline ModInt& operator-=(ModInt x) noexcept {
        if ((value -= x.value) < 0) value += MOD;
        return *this;
    }
    inline ModInt& operator*=(ModInt x) noexcept {
        value = (value * x.value) % MOD; return *this;
    }
    inline ModInt& operator/=(ModInt x) noexcept {
        value = (value * x.inv().value) % MOD; return *this;
    }

    inline ModInt operator+(ModInt x) const noexcept { return ModInt(*this) += x; }
    inline ModInt operator-(ModInt x) const noexcept { return ModInt(*this) -= x; }
    inline ModInt operator*(ModInt x) const noexcept { return ModInt(*this) *= x; }
    inline ModInt operator/(ModInt x) const noexcept { return ModInt(*this) /= x; }
    inline bool operator==(ModInt x) const noexcept { return value == x.value; }
    inline bool operator!=(ModInt x) const noexcept { return !(this->operator==(x)); }

    friend ostream& operator<<(ostream &os, ModInt x) noexcept { os << x.value; return os; }
    friend istream& operator>>(istream &is, ModInt &x) noexcept { is >> x.value; x.value %= MOD; return is; }

    static constexpr inline ModInt pow(int64_t n, int64_t p) noexcept {
        int64_t ret = 1;
        for(; p > 0; p >>= 1) {
            if (p & 1) ret = (ret * n) % MOD;
            n = (n * n) % MOD;
        }
        return ret;
    }
};
// }}}
using modint = ModInt<MOD>;

// Factorial, InvFact {{{
template<size_t N, int MOD>
struct Factorial {
    uint_fast64_t f[N+1];

    inline Factorial() : f{1} {
        for (int i = 1; i <= N; ++i) f[i] = (f[i-1] * i) % MOD;
    }

    constexpr inline ModInt<MOD> operator[] (size_t i) const { return f[i]; }
};

template<size_t N, int MOD>
struct InvFact {
    uint_fast64_t inv[N+1];
    uint_fast64_t f[N+1];

    inline InvFact() : inv{0, 1}, f{1, 1} {
        for (int i = 2; i <= N; ++i) {
            inv[i] = (MOD - MOD/i) * inv[MOD % i] % MOD;
            f[i] = f[i-1] * inv[i] % MOD;
        }
    }

    constexpr inline ModInt<MOD> operator[] (size_t i) const { return f[i]; }
};
// }}}
Factorial<1000100, MOD> fact;
InvFact<1000100, MOD> invFact;
ModInt<MOD> nCr(int n, int r) { return (r < 0 || n < r) ? 0 : (fact[n] * (invFact[r] * invFact[n-r])); }
ModInt<MOD> nPr(int n, int r) { return (r < 0 || n < r) ? 0 : (fact[n] * invFact[n-r]); }
ModInt<MOD> nHr(int n, int r) { return nCr(n+r-1, r); }

signed main() {
    ios_base::sync_with_stdio(false); cin.tie(nullptr);

    i64 r1, c1, r2, c2;
    read(r1, c1, r2, c2);

    modint ans = 0;
    reps(y, r1, r2) {
        const i64 h = y;
        const auto f = [&h](i64 w) -> modint {
            return (modint(w+1) * fact[w+h+1]) / (modint(h+1) * fact[w+1] * fact[h]);
        };
        ans += f(c2) - f(c1-1);
    }

    print(ans);

    return 0;
}