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;
#define rep(i,n) for(int i=0; i<(n); i++)
using ll = long long;
constexpr int MX = 2000005, MOD = 1e9+7;
int r1, r2, c1, c2;
ll ans;
ll exp(ll b, ll n){
	ll res = 1;
	for(; n; n/=2,(b*=b)%=MOD) if(n%2) (res *= b) %= MOD;
	return res;
}
ll fact[MX] = {1}, invf[MX];
void setcomb(int n){
	for(int i = 1; i <= n; i++) fact[i] = (fact[i-1] * i) % MOD;
	invf[n] =  exp(fact[n] ,MOD-2);
	for(int i = n; i > 0; i--) invf[i-1] = (invf[i] * i) % MOD;
}
inline ll comb(int a, int b){return fact[a] * invf[a-b] % MOD * invf[b] % MOD;}
int main(){
	scanf("%d%d%d%d", &r1, &c1, &r2, &c2);
	r2++; c2++;
	setcomb(r2+c2);
	ans = (comb(r2+c2,r2) - comb(r2+c1,r2) - comb(r1+c2,r1) + comb(r1+c1,r1)) % MOD;
	if(ans < 0) ans += MOD;
	printf("%lld\n", ans);
}