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 CPP):

Solution:
#include<bits/stdc++.h>
#define forn(i,a,b)for(int i=(a),_b=(b);i<=_b;i++)
#define fore(i,b,a)for(int i=(b),_a=(a);i>=_a;i--)
#define rep(i,n)for(int i=0,_n=n;i<n;i++)
#define ll long long
#define pii pair<int,int>
#define m_p make_pair
#define pb push_back
#define fi first
#define se second
#define foreach(i,c) for(__typeof(c.begin())i=(c.begin());i!=(c).end();i++)
#define int ll
using namespace std;
const int N=110;
const int mod=1000000007;
int n,m;
int c[N],b[N];
int f;
int dp[N][N*100];
int ans=0;
int l,r;
signed main(){
    cin>>n;
	forn(i,1,n)
		cin>>c[i];
    forn(i,2,n){
    	cin>>b[i];
    	b[i]+=b[i-1];
	}
	cin>>m>>f;
    dp[0][0]=1;l=r=0;
    forn(i,1,n){
        l+=b[i]+f;r+=c[i];
        forn(j,max(l,0ll),r){
        	forn(k,0,c[i]){
        		if(j-k>=0)dp[i][j]=(dp[i][j]+dp[i-1][j-k])%mod;
			}
		}
    }
    forn(i,max(l,0ll),r)
		ans=(ans+dp[n][i])%mod;
	cout<<ans<<"\n";
    return 0;
}