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;
const ll mod = 1e9 + 7;
const int maxn = 2e6 + 10;
ll fac[maxn], inv[maxn], facinv[maxn];
ll norm(ll x) { return (x % mod + mod) % mod;}
void pre()
{
	fac[0] = 1; for(int i = 1; i < maxn; ++i) fac[i] = fac[i - 1] * i % mod;
	inv[1] = 1; for(int i = 2; i < maxn; ++i) inv[i] = (mod - mod / i) * inv[mod % i] % mod;
	facinv[0] = 1; for(int i = 1; i < maxn; ++i) facinv[i] = facinv[i - 1] * inv[i] % mod;
}
ll C(int n, int m) { return fac[n] * facinv[m] % mod * facinv[n - m] % mod;};
ll f(int x, int y)
{
	ll ans = 0;
	for(int i = 0; i <= x; ++i) ans = norm(ans + C(i + 1 + y, y));
	return ans;
}
int main()
{
	pre();
	int r1, c1, r2, c2;
	cin >> r1 >> c1 >> r2 >> c2;
	ll ans = f(r2, c2) - f(r1 - 1, c2) - f(r2, c1 - 1) + f(r1 - 1, c1 - 1);
	ans = norm(ans);
	printf("%lld\n", ans);
	return 0;
}