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;
typedef long long ll;
const int mod = 1000000007;
ll fac[2000005];
ll invfac[2000005];
ll inv[2000005];
inline ll exp(int a, int x ){
    if (x == 0) return 1;
    ll p = exp(a,x/2);
    p *= p;
    p %= mod;
    if (x % 2 == 1){
        p *= a;
        p %= mod;
    }
    return p;
}
inline ll ways(int r, int c){
    return (((fac[r+c]*invfac[r])%mod)*invfac[c])%mod;
}
int main(){
    int r1,r2,c1,c2;
    scanf("%d%d%d%d",&r1,&c1,&r2,&c2);
    fac[0] = invfac[0] = 1;
    for (int i = 1; i <= r2+c2+2; i++){
        fac[i] = (fac[i-1]*i)%mod;
        inv[i] = exp(i,mod-2);
        invfac[i] = (invfac[i-1]*inv[i])%mod;
    }
    ll ans = (ways(r2+1,c2+1) - ways(r2+1,c1) - ways(r1,c2+1) + ways(r1,c1) + mod)%mod;
    printf("%lld ",ans);
}
