Problem: This is the easy version of the problem. The only difference is that in this version q = 1. You can make hacks only if both versions of the problem are solved.

There is a process that takes place on arrays a and b of length n and length n-1 respectively. 

The process is an infinite sequence of operations. Each operation is as follows: 

  * First, choose a random integer i (1 ≤ i ≤ n-1). 
  * Then, simultaneously set a_i = min\left(a_i, \frac{a_i+a_{i+1}-b_i}{2}\right) and a_{i+1} = max\left(a_{i+1}, \frac{a_i+a_{i+1}+b_i}{2}\right) without any rounding (so values may become non-integer). 

See notes for an example of an operation.

It can be proven that array a converges, i. e. for each i there exists a limit a_i converges to. Let function F(a, b) return the value a_1 converges to after a process on a and b.

You are given array b, but not array a. However, you are given a third array c. Array a is good if it contains only integers and satisfies 0 ≤ a_i ≤ c_i for 1 ≤ i ≤ n.

Your task is to count the number of good arrays a where F(a, b) ≥ x for q values of x. Since the number of arrays can be very large, print it modulo 10^9+7.

Input

The first line contains a single integer n (2 ≤ n ≤ 100).

The second line contains n integers c_1, c_2 …, c_n (0 ≤ c_i ≤ 100).

The third line contains n-1 integers b_1, b_2, …, b_{n-1} (0 ≤ b_i ≤ 100).

The fourth line contains a single integer q (q=1).

The fifth line contains q space separated integers x_1, x_2, …, x_q (-10^5 ≤ x_i ≤ 10^5).

Output

Output q integers, where the i-th integer is the answer to the i-th query, i. e. the number of good arrays a where F(a, b) ≥ x_i modulo 10^9+7.

Example

Input


3
2 3 4
2 1
1
-1


Output


56

Note

The following explanation assumes b = [2, 1] and c=[2, 3, 4] (as in the sample).

Examples of arrays a that are not good: 

  * a = [3, 2, 3] is not good because a_1 > c_1; 
  * a = [0, -1, 3] is not good because a_2 < 0. 



One possible good array a is [0, 2, 4]. We can show that no operation has any effect on this array, so F(a, b) = a_1 = 0.

Another possible good array a is [0, 1, 4]. In a single operation with i = 1, we set a_1 = min((0+1-2)/(2), 0) and a_2 = max((0+1+2)/(2), 1). So, after a single operation with i = 1, a becomes equal to [-1/2, 3/2, 4]. We can show that no operation has any effect on this array, so F(a, b) = -1/2.

Solution (in PYTHON3):

Solution:
def putin():
    return map(int, input().split())


def sol():
    n = int(input())
    C = list(putin())
    B = list(putin())
    q = int(input())
    x = int(input())
    min_arr = [x]
    min_part_sums = [x]
    part_sums = [C[0]]
    for i in range(1, n):
        part_sums.append(part_sums[-1] + C[i])
    for elem in B:
        min_arr.append(min_arr[-1] + elem)
        min_part_sums.append(min_arr[-1] + min_part_sums[-1])
    for i in range(n):
        if min_part_sums[i] > part_sums[i]:
            return 0
    if min_part_sums[0] > C[0]:
        return 0
    answer = [1] * (part_sums[0] - max(0, min_part_sums[0]) + 1)
    for k in range(1, n):
        new_answer = [0] * (part_sums[k] - max(0, min_part_sums[k]) + 1)
        cnt = 1
        window = answer[-1]
        new_answer[-1] = window
        while cnt <= len(new_answer) - 1:
            cnt += 1
            if cnt <= len(answer):
                window += answer[-cnt]
            if C[k] + 1 < cnt:
                window -= answer[C[k] + 1 - cnt]
            new_answer[-cnt] = window
        answer = new_answer.copy()
    m = 10 ** 9 + 7
    return sum(answer) % m


print(sol())