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 int long long int
#define until(x) while(!(x))
#define unless(x) if(!(x))
#define all(x) (x).begin(),(x).end()
#define F first
#define S second
#define pc __builtin_popcount
const int mod = 1e9+7;

int fac[2000050];

int pw(int base, int expo){
	if(!expo){
		return 1;
	}
	int k = pw(base,expo/2);
	k*=k;
	k%=mod;
	if(expo&1){
		k*=base;
		k%=mod;
	}
	return k;
}

int inv(int n){
	return pw(n,mod-2);
}

int comb(int n, int r){
	return (((fac[n]*inv(fac[r]))%mod)*inv(fac[n-r]))%mod;
}

int32_t main(){
	fac[0]=1;
	for(int i=1;i<=2e6+10;i++){
		fac[i]=i*fac[i-1];
		fac[i]%=mod;
	}
	int r1,r2,c1,c2;
	cin>>r1>>c1>>r2>>c2;
	int ans = comb(r2+c2+2,r2+1);
	ans -= comb(r2+c1+1,r2+1);
	ans -= comb(r1+c2+1,r1);
	ans += comb(r1+c1,r1);
	ans += mod;
	ans %= mod;
	cout<<ans;
}
