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<cstdio>

typedef long long ll;

const ll mod=1e9+7;
ll jc[3000010]={1,1};
ll in[3000010]={1,1};

ll pow(ll a,ll b)
{
	ll ans = 1;
	while(b > 0){
		if(b & 1)
			ans = ans * a % mod;
		a = a * a % mod;
		b>>=1;
	}
	return ans;
}
inline ll inv(ll x){return pow(x,mod-2);}
ll C(ll r,ll c){return jc[r+c]*in[r]%mod*in[c]%mod;}

int main()
{
	ll r1,c1,r2,c2;
	scanf("%lld%lld%lld%lld",&r1,&c1,&r2,&c2);
	for(ll i=1;i<=3000000;i++) jc[i]=jc[i-1]*i%mod,in[i]=inv(jc[i]);
	ll ans=0;
	for(ll r=r1;r<=r2;r++)
	{
		ans+=((C(r+1,c2)-C(r+1,c1-1))%mod+mod)%mod;
		ans%=mod;
	}
	printf("%lld\n",ans);
	return 0;
}
