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<iostream>
#include<queue>
#include<cmath>
#include<cstdio>
#include<cstring>
#define INF 0x3f3f3f3f
#define LL long long
using namespace std;
int const maxn = 2e6+100;
int const mod = 1e9+7;
LL fac[maxn];
LL qpow(LL a, LL b){
	LL ans = 1;
    while (b) {
        if (b & 1)
            ans = ans * a % mod;
        a = a * a % mod;
        b >>= 1;
    }
    return ans;
}
LL C(LL n, LL m){
	return fac[n] * qpow(fac[m], mod-2) % mod * qpow(fac[n-m], mod-2) % mod;
}
int main(){
	fac[0] = fac[1] = 1;
	for(int i = 2; i < maxn; i++)
		fac[i] = fac[i-1] * i % mod;
	LL r1, r2, c1, c2;
	scanf("%lld %lld %lld %lld", &r1, &c1, &r2, &c2);
	LL res=C(r2+c2+2, c2+1) + C(r1+c1, c1) - C(r2+c1+1, c1) - C(r1+c2+1, c2+1);
	res = (res % mod + mod) % mod;
	printf("%lld\n", res%mod);
	return 0;
}