Problem: This is the hard version of the problem. The only difference is that in this version 1 ≤ q ≤ 10^5. 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 (1 ≤ q ≤ 10^5).

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
5
-1 0 1 -100000 100000


Output


56
28
4
60
0

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>
using namespace std;
typedef long long ll;
const int M=1e9+7;
void add(int &A,int B){
	A+=B;
	if(A>=M)A-=M;
}
int f[10004],g[10004],sum,sb;
int n,q,x,c[103],b[103],pans=1;
int l=1e9,r=1e9;
int mp[103];
void solve(int x){
	memset(f,0,sizeof(f));
	sum=sb=0;
	f[0]=1;
	for(int i=1;i<=n;i++){
		sum+=b[i-1],sb+=sum;
		memset(g,0,sizeof(g));
		for(int j=0;j<=i*100;j++)g[j]=g[j-1],add(g[j],f[j]);
		for(int j=0;j<=i*100;j++){
			f[j]=g[j];
			if(j>c[i])add(f[j],M-g[j-c[i]-1]);
		}
		for(int j=0;j<min(sb+i*x,i*100+1);j++)f[j]=0;
	}
	int ans=0;
	for(int i=0;i<=n*100;i++)add(ans,f[i]);
	mp[x-l]=ans;
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",&c[i]),pans=(ll)pans*(c[i]+1)%M;
	for(int i=1;i<n;i++)scanf("%d",&b[i]);
	for(int i=1;i<=n;i++){
		sum+=b[i-1],sb+=sum;
		l=min(l,-((sb-1)/i+1)),r=min(r,(100*n-1-sb)/i+1);
	}
	for(int i=l;i<=r;i++)solve(i);
	scanf("%d",&q);
	while(q--){
		scanf("%d",&x);
		if(x<l)printf("%d\n",pans);
		else if(x>r)puts("0");
		else printf("%d\n",mp[x-l]);
	}
}