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>
#define MOD 1000000007
#define ll long long
#define mp make_pair
#define pb push_back 
using namespace std;
ll fact[2000100];
ll moduloexp(ll a,ll b){
	ll res=1;
	while(b){
		if(b&1)res=(1LL*res*a)%MOD;
		b/=2;
		a=(1LL*a*a)%MOD;
	}
	return res;
}
ll comb(ll n,ll r){
	if(n<r)
		return 0;  
	return (1LL*fact[n]*moduloexp((1LL*fact[n-r]*fact[r])%MOD,MOD-2))%MOD;
}
void init(){
	fact[0]=1;
	for(int i=1;i<2000010;i++)
		fact[i]=(fact[i-1]*i)%MOD;
}
int main(){
	ios::sync_with_stdio(false);
	cin.tie(NULL);
	init();
	int r1, r2, c1, c2;
	cin >> r1 >> c1 >> r2 >> c2;
	ll ans = 0;
	for(int i = r1; i <= r2; i++){
		ans = (ans + comb(i + c2 + 1, i + 1) - comb(i + c1, i + 1) + MOD) % MOD;
		//cout << ans << '\n';
	}
	cout << ans << '\n';

}