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,x,y) for(int i=x;i<y;i++)
#define range(a) (a).begin(),(a).end()
#define print(A,x,n) rep(i,0,n){cout<<(i ? " ":"")<<A[i]x;}cout<<endl;
#define pprint(A,y,m,n) rep(j,0,m){print(A[j],y,n);}
const long mod=1e9+7;
const int size=2e6+5;
const int inf=1e9;
long fact[size];
void calc(long n){
	fact[0] = 1;
	rep(i,1,n) fact[i] = fact[i-1] * i % mod;
	return;
}
long modcomb(long n, long r){
	n += r;
	if(n < r) return 0;
	long x = (fact[n-r] * fact[r]) % mod;
	long res = 1; int i = 0;
	while( (mod-2) >= (1<<i) ){
		if( (mod-2) & (1<<i) ) (res *= x) %= mod;
		i++; x = x * x % mod;
	}return res * fact[n] % mod;
}
int main(){
	long a,b,c,d; cin>>a>>b>>c>>d;
	calc(size);
	long ans = modcomb(c+1, d+1) - modcomb(a, d+1) - modcomb(c+1, b) + modcomb(a, b);
	cout<<(ans % mod + mod) % mod<<endl;
}