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
#pragma GCC optimize(2)
#include<bits/stdc++.h>
#define ll long long
#define maxn 2000005
#define inf 1e9
#define eps 1e-10
using namespace std;

ll r1,c1,r2,c2,fac[maxn],inv[maxn];
const ll mod=1e9+7;

inline ll qpow(ll a,ll b)
{
	ll ans=1,base=a;
	while(b)
	{
		if(b&1) ans=(ans*base)%mod;
		base=(base*base)%mod; b>>=1;
	}
	return ans;
}

inline ll C(ll n,ll m){return ((fac[n]*inv[m])%mod*inv[n-m])%mod;}
inline ll F(ll a,ll b)
{
	ll res=0;
	for(int i=1;i<=b+1;i++) res=(res+C(a+i,i)%mod);
	return res;
}

int main()
{
	cin>>r1>>c1>>r2>>c2; fac[0]=1; inv[0]=1;
	for(int i=1;i<=maxn-4;i++) fac[i]=(i*fac[i-1])%mod;
	for(int i=1;i<=maxn-4;i++) inv[i]=qpow(fac[i],mod-2);
	ll p1=F(r2,c2)-F(r1-1,c2)-F(r2,c1-1)+F(r1-1,c1-1);
	p1=(p1%mod+mod)%mod; cout<<p1<<endl;
	return 0;
}