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;

typedef long long ll;
ll m = 1000000007;
ll factorials[2000005];

ll modexp(ll n, ll e){
	if (e==0){
		return 1;
	}
	if (e%2==0){
		ll ans = modexp(n,e/2);
		return (ans*ans)%m;
	} else {
		ll ans = modexp(n,(e-1)/2);
		return (((ans*ans)%m)*n)%m;
	}
}

ll inv(ll n){
	return modexp(n,m-2);
}

ll ncr(ll n, ll r){
	ll ans = factorials[n];
	ans=ans*inv(factorials[r]);
	ans%=m;
	ans=ans*inv(factorials[n-r]);
	ans%=m;
	return ans;
}

int main(){
	ll r1,c1,r2,c2;
	cin>>r1>>c1>>r2>>c2;
	factorials[0]=1;
	for (int i = 1; i<2000005; i++){
		factorials[i]=(factorials[i-1]*i)%m;
	}
	ll ans;
	ans=ncr(r1+c1,r1)+ncr(r2+c2+2,r2+1);
	ans%=m;
	ans-=ncr(r2+c1+1,c1);
	ans+=m;
	ans%=m;
	ans-=ncr(r1+c2+1,r1);
	ans+=m;
	ans%=m;
	cout<<ans<<endl;
	return 0;
}