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 ll long long
#define MOD 1000000007
using namespace std;
int r1, r2, c1, c2;
ll ans, arr[2000020];
ll g(int, int);
ll f(int, int);
ll cal(ll, int);
int main()
{
	ios::sync_with_stdio(false);
	arr[0] = 1;
	for(int i = 1; i<=2000010; ++i) arr[i] = arr[i-1]*(ll)i%MOD;
    cin>>r1>>c1>>r2>>c2;
	ans = g(r2, c2)-g(r1-1, c2)-g(r2, c1-1)+g(r1-1, c1-1);
	//ans = (ans+MOD)%MOD;
	ans%=MOD;
	if(ans<0) ans+=MOD;
	cout<<ans<<"\n";
}

ll g(int a, int b)
{
	ll sum = 0;
	for(int i = 1; i<=a+1; ++i) 
		//sum+=f(i, b)%MOD;
		(sum+=f(i, b))%=MOD;
	return sum;
}

ll f(int a, int b)
{
	//(a+b)!/a!/b!;
	return arr[a+b]*cal(arr[a], MOD-2)%MOD*cal(arr[b], MOD-2)%MOD;
}

ll cal(ll a,int b) {
	if (b==0) return 1;
	if (b%2==1) return a*cal(a*a%MOD,b/2)%MOD;
	else return cal(a*a%MOD,b/2);
}