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;
const int mod = 1e9+7;
long long f1[3000000], f2[3000000];
long long p(long long a, long long b = mod-2){
    long long ans = 1;
    while(b){
        if(b%2 == 1) ans = ans*a%mod;
        a = a*a%mod;
        b/=2;
    }
    return ans;
}
long long ncr(int a, int b){
    return f1[a]*f2[b]%mod*f2[a-b]%mod;
}
int main(){
    f1[0] = f2[0] = 1;
    for(int i=1;i<3000000;i++){
        f1[i] = f1[i-1]*i%mod;
        f2[i] = p(f1[i]);
    }
    int r1, c1, r2, c2;
    scanf("%d%d%d%d", &r1, &c1, &r2, &c2);
    long long ans = 0;
    for(int i=r1;i<=r2;i++){
        long long res = ((ncr(i+c2+1, i+1) - ncr(i+c1+1, i+1) + mod)%mod + ncr(i+c1, i))%mod;
        ans = (ans + res)%mod;
    }
    printf("%lld\n", ans);
}