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 facinv(N):
    fac,finv,inv=[0]*(N+1),[0]*(N+1),[0]*(N+1)
    fac[0]=1;fac[1]=1;finv[0]=1;finv[1]=1;inv[1]=1
    for i in range(2,N+1):
        fac[i]=fac[i-1]*i%MOD
        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD
        finv[i]=finv[i-1]*inv[i]%MOD
    return fac,finv,inv

def COM(n,r):
    if n<r or r<0:
        return 0
    else:
        return ((fac[n]*finv[r])%MOD*finv[n-r])%MOD
        
r1,c1,r2,c2=map(int,input().split())

fac,finv,inv=facinv(r2+c2+1)

ans=0

for i in range(r1,r2+1):
    ans=(ans+COM(c2+i+1,i+1)-COM(c1+i,i+1)+MOD)%MOD
print(ans)