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>
using namespace std;
#define REP(i, init, n) for(int i = (int)(init); i < (int)(n); i++)
long long MOD = 1000000007;
long long MODPOW(long long inv,long long pow, long long mod){
    if(pow == 1) return inv % mod;
    else{
        if(pow % 2) return inv * MODPOW(inv, pow -1, mod) % mod;
        long long res = MODPOW(inv, pow/2, mod);
        return res * res % mod; 
    }
}

long long COMMOD(int a, int b){
    long long res=1; long long resinv = 1;
    for(int i = a; i>a-b; i--){
        res = res * i % MOD;
        resinv = resinv*(a-i+1) % MOD;
    }
    return res*MODPOW(resinv, MOD-2, MOD) % MOD;
}

int main() {
    int r1, c1, r2, c2;
    cin >> r1 >> c1 >> r2 >> c2;
    long ans = 0;
    ans = COMMOD(r2 + c2 + 2, c2 + 1) - COMMOD(r1 + c2 + 1, c2 + 1) - (COMMOD(r2 + c1 + 1, c1) - COMMOD(r1 + c1, c1));
    if(ans < 0) ans += MOD * 2;
    ans %= MOD;
    cout << ans << endl;
}