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"
#include<cassert>
using namespace std;
#define int long long
#define rep(i,n) for(int i=0;i<n;i++)
const int mod = 1000000007;
const int inf = 1ll << 61;
const int maxN = 4e6 + 2;
typedef pair<int, int> P;
typedef pair<int, P>PP;
struct edge {
	int to, cost;
};

int kj[maxN], kji[maxN];
int modpow(int a, int x, int mod) {
	int res = 1;
	while (x) {
		if (x & 1)res = res*a%mod;
		x >>= 1;
		a = a*a%mod;
	}
	return res;
}
void setkj(int n) {
	kj[0] = 1;
	rep(i, n)kj[i + 1] = kj[i] * (i + 1) % mod;
	rep(i, n + 1)kji[i] = modpow(kj[i], mod - 2, mod);
}
int comb(int r, int c) {
	if (c<0 || r<c)return 0;
	return kj[r] * kji[c] % mod*kji[r - c] % mod;
}
signed main() {
	int r1, c1, r2, c2; cin >> r1 >> c1 >> r2 >> c2;
	setkj(r2 + c2+2);
	int res = comb(r2 + c2 + 2, r2 + 1) + comb(r1 + c1 , r1) - comb(r1 + c2 + 1, r1) - comb(r2 + c1 + 1, c1);
	cout << (res+mod*3)%mod << endl;
}