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;
typedef long long ll;
#define UP 2000005
#define mod 1000000007
ll pw[UP] = {0, 1};
ll inv[UP] = {1, 1};
ll modinv(ll a, ll p) {
    if (p == 1) return 0;
    ll pp = p, y = 0, x = 1;
    while (a > 1) {
        ll q = a / p, t = p;
        p = a % p, a = t, t = y, y = x - q * y, x = t;
    }
    if (x < 0) x += pp;
    return x;
}
void init() {
	for (int i = 2; i < UP; i++) {
		pw[i] = pw[i-1] * i % mod;
		inv[i] = modinv(pw[i], mod);
		//cout <<  i << " " << pw[i] << " " << inv[i] << "\n";
	}
}
ll C(int a, int b) {
	return pw[a] * inv[a-b] % mod * inv[b] % mod;
}
int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int r1, c1, r2, c2;
	cin >> r1 >> c1 >> r2 >> c2;
	init();
	ll ans = 0;
	for (int x = r1; x <= r2; x++) {
		ans = (ans + C(c2 + x + 1, x + 1)) % mod;
		ans = (ans + mod - C(c1 + x, x + 1)) % mod;
	}
	cout << ans << "\n";
	return 0;
}