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).

Examples

Input

1 1 2 2


Output

14


Input

314 159 2653 589


Output

602215194
#include <bits/stdc++.h>

int main() {
    using namespace std;
    constexpr unsigned long MOD = 1000000007;
    unsigned long r1, r2, c1, c2;
    cin >> r1 >> c1 >> r2 >> c2;
    ++r2;
    ++c2;
    unsigned long N{r2 + c2};
    vector<unsigned long> factmod(N + 1, 1);
    for(unsigned long i{1}; i <= N; ++i)factmod[i] = factmod[i - 1] * i % MOD;
    const auto& binom = [&factmod](unsigned long k, unsigned long c) -> unsigned long {
        unsigned long r{factmod[k + c]}, a{factmod[k] * factmod[c] % MOD}, n{MOD - 2};
        while(n){
            if(n & 1)(r *= a) %= MOD;
            (a *= a) %= MOD;
            n >>= 1;
        }
        return r;
    };
    unsigned long f11{binom(r1, c1)}, f12{binom(r1, c2)}, f21{binom(r2, c1)}, f22{binom(r2, c2)};
    cout << (MOD * 2 + f22 + f11 - f12 - f21) % MOD << endl;
    return 0;
}