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=1000000007
def fact(x):
    k=1
    for i in range(x+1):
        if i!=0:
            k=(k*i)%MOD
    return k

def inverse(b):
    r=1;e=MOD-2
    while e:
        if (e%2==1):
            r = (r*b)%MOD
        b=(b*b)%MOD
        e>>=1
    return r

def Comb(i,j):
    if i==0 or j==0:
        return 0
    num=fact(i+j)
    num*=inverse(fact(i))
    num%=MOD
    num*=inverse(fact(j))
    num%=MOD
    return num
    
r1,c1,r2,c2 = map(int,input().split())
#おなじみパスカル行列を区間で和を取ろうという問題
#F[n][r]=nCr(n+r,r)と、
#G[a][b]をΣ[i,0~a-1](Σ[j,0~b-1](F[i][j]))と表す
#ここで、G[a][b]をO(N)くらいで計算できれば勝ち
#ところで、G[a][b]=F[a+1][b+1]-1になる
#なので、それぞれのGをO(N+logMOD)で計算できるのでAC
Ans=0
Ans+=Comb(r2+1,c2+1)
Ans-=Comb(r1,c2+1)
Ans-=Comb(r2+1,c1)
Ans+=Comb(r1,c1)
Ans+=MOD;Ans+=MOD;Ans%=MOD

print(Ans)