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
mod = 10**9+7
def cmb(n,k):
    return fac[n]*inv_fac[n-k]*inv_fac[k] % mod
def g(r,c):
    x = 0
    for i in range(1,r+2):
        x += cmb(c+i,i)
    x %= mod
    return x

r1,c1,r2,c2 = map(int,input().split())
N = r2+c2+1
fac = [1]
for i in range(1,N+1):
    fac.append(fac[-1]*i % mod)
inv_fac = [pow(fac[N],mod-2,mod)]
for i in range(1,N+1)[::-1]:
    inv_fac.append(inv_fac[-1]*i % mod)
inv_fac = inv_fac[::-1]
print((g(r2,c2)-g(r2,c1-1)-g(r1-1,c2)+g(r1-1,c1-1))% mod)