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;
const ll mod=1000000007;
ll nj[2000003]={0};
ll c1,c2,r1,r2;
ll qpow(ll a,ll b)
{
	if(b==0)	return 1;
	ll c=qpow(a,b/2);
	if(b%2==0)	return c*c%mod;
	else		return c*c%mod*a%mod;
}
ll cnm(ll n,ll m)
{
	return nj[m+n]*qpow(nj[n]*nj[m]%mod,mod-2)%mod;
}
ll f()
{
	return cnm(r1,c1)+cnm(r2+1,c2+1)-cnm(r1,c2+1)-cnm(r2+1,c1);
}
int main(void)
{
	scanf("%lld%lld%lld%lld",&r1,&c1,&r2,&c2);
	nj[0]=1;
	for(ll i=1;i<=2000002;i++)
	{
		nj[i]=nj[i-1]*i;
		nj[i]%=mod;
	}
	printf("%lld",(f()+mod*100)%mod);
}