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 pii pair<int,int> 
#define mp make_pair
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define all(c) c.begin(),c.end()
#define pb push_back
#define fi first
#define se second
#define chmin(x,y) x=min(x,y)
#define chmax(x,y) x=max(x,y)
#define mod 1000000007
using namespace std;
ll inv[2000005];
int r1,c1,r2,c2;
void init(){
    inv[1]=1;
    for(int i=2;i<=2000003;i++)
        inv[i]=1ll*(mod-mod/i)*inv[mod%i]%mod;
}
ll C(int n,int k){
	ll ans=1;
	for (int i=1;i<=n;i++)
		ans=ans*i%mod;
	for(int i=1;i<=k;i++)
		ans=ans*inv[i]%mod;
	for(int i=1;i<=n-k;i++)
		ans=ans*inv[i]%mod;
	return ans;
}
int main(){
    init();
 	cin>>r1>>c1>>r2>>c2;
	ll ans=0;
	ans=C(c2+r2+2,c2+1)+C(c1+r1,c1)+mod*2-C(c2+r1+1,c2+1)-C(c1+r2+1,c1);
	ans%=mod;
	cout<<ans<<endl;
	return 0;
}