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>
using namespace std;
typedef unsigned int ui;
typedef long long ll;
typedef unsigned long long ull;
typedef double db;
typedef long double ldb;
#define range(x) (x).begin(),(x).end()
std::mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
inline int sj(int n)
{
	unsigned int x=rnd();
	return x%n+1;
}
#define rand fst
template<typename typC> void read(register typC &x)
{
	register int c=getchar(),fh=1;
	while ((c<48)||(c>57))
	{
		if (c=='-') {c=getchar();fh=-1;break;}
		c=getchar();
	}
	x=c^48;c=getchar();
	while ((c>=48)&&(c<=57))
	{
		x=x*10+(c^48);
		c=getchar();
	}
	x*=fh;
}
template<typename typC> void read(register typC *a,int num)
{
	for (register int i=1;i<=num;i++) read(a[i]);
}
template<typename typC, typename... Args> void read(typC &first, Args& ... args) {
	read(first);
	read(args...);
}
template<typename typC> void write(register typC x)
{
	if (x<0) putchar('-'),x=-x;
	static int st[100];
	register int tp=1;
	register typC y;st[1]=x%10;x/=10;
	while (x) y=x/10,st[++tp]=x-y*10,x=y;++tp;
	while (--tp) putchar(st[tp]|48);
}
template<typename typC> void write(register typC *a,register int num)
{
	for (register int i=1;i<=num;i++) write(a[i]),putchar(i==num?10:32);
}
template<typename typC> typC ab(register typC x)
{
	if (x<0) return -x;
	return x;
}
#define space(x) write(x),putchar(32)
#define enter(x) write(x),putchar(10)
const int p=1e9+7;
const db eps=1e-9;
inline void inc(register int &x,const int y)
{
	if ((x+=y)>=p) x-=p;
}
inline void dec(register int &x,const int y)
{
	if ((x-=y)<0) x+=p;
}
inline int ksm(register int x,register int y)
{
	register int r=1;
	while (y)
	{
		if (y&1) r=(ll)r*x%p;
		x=(ll)x*x%p;
		y>>=1;
	}
	return r;
}
priority_queue<int> ONLYYFORRCOPYY;
priority_queue<int,vector<int>,greater<int> > ONLYYFORRCOPYY__;
struct Q
{
	int u,v;
	Q(int a=0,int b=0):u(a),v(b){}
	bool operator<(const Q &o) const {return v<o.v;}
};
const int N=1e2+2,M=2e4+20,inf=1e9;
char s[N];
int a[N],b[N],l[N],r[N],L[N],R[N],g[N][M],*f[N];
int T,n,m,i,j,k,ii,x,y,z,ans,la,ksiz,ks,q,cur;
int main()
{
	//ios::sync_with_stdio(false);
	cout<<setiosflags(ios::fixed)<<setprecision(15);
	T=1;
	read(n,r,n);read(b,n-1);
	for (i=2;i<n;i++) b[i]+=b[i-1];
	for (i=2;i<=n;i++) r[i]-=b[i-1],l[i]-=b[i-1];
	read(q);read(q);cur=0;
	for (i=1;i<=n;i++) L[i]=L[i-1]+l[i],R[i]=R[i-1]+r[i];
	//for (i=1;i<=n;i++) printf("%d %d\n",l[i],r[i]);puts("");
	for (i=0;i<=n;i++) cur+=l[i],f[i]=&(g[i][-cur+2]);
	f[0][0]=1;
	for (i=1;i<=n;i++) for (j=max(q*i,L[i]);j<=R[i];j++) for (k=l[i];k<=r[i];k++) if (j-k>=L[i-1]&&j-k<=R[i-1]) inc(f[i][j],f[i-1][j-k]);
	//for (i=0;i<=n;i++) for (j=L[i];j<=R[i];j++) printf("%d %d %d\n",i,j,f[i][j]);
	for (i=L[n];i<=R[n];i++) inc(ans,f[n][i]);write(ans);
}