Sunuke received a d-dimensional hypercube with a side length of l1 × ... × ld as a birthday present. Sunuke placed this rectangular parallelepiped so that the range of the i-th coordinate was 0 or more and li or less, and ate the part that satisfied x1 + ... + xd ≤ s. However, xi represents the i-th coordinate. If the volume of the part eaten by Sunuke is V, it can be proved that d! V (V multiplied by the factorial of d) is an integer. Find the remainder of d! V divided by 1,000,000,007.

Constraints

* 2 ≤ d ≤ 300
* 1 ≤ li ≤ 300
* 0 ≤ s ≤ $ \ sum l_ {i} $
* All inputs are integers

Input


d
l1
.. ..
ld
s


Output

Output d! V divided by 1,000,000,007.

Examples

Input

2
6
3
4


Output

15


Input

5
12
34
56
78
90
123


Output

433127538
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<double,int> P;
typedef pair<P,ll> T;
typedef vector<int> vi;
typedef vector<ll> vll;
#define pb push_back
#define mp make_pair
#define eps 1e-15
#define INF 2000000000
#define sz(x) ((int)(x).size())
#define fi first
#define sec second
#define all(x) (x).begin(),(x).end()
#define rep(i,n) for(int (i)=0;(i)<(int)(n);(i)++)
#define repn(i,a,n) for(int (i)=(a);(i)<(int)(n);(i)++)
#define EQ(a,b) (abs((a)-(b))<eps)
template<class T> void chmin(T& a,const T& b){if(a>b)a=b;}
template<class T> void chmax(T& a,const T& b){if(a<b)a=b;}
#define MOD 1000000007ll // prime
// How to devide :
// ModInt a(6ll);
// ModInt b(2ll);
// a *= b.exp(MOD-2ll);  -> a/=b;  result: a = 3
struct ModInt{
	ll val;
	ModInt():val(0ll){}
	ModInt(ll v):val(((v%MOD)+MOD)%MOD){}
	ModInt exp(ll y)const{
		if(!y)return ModInt(1ll);
		ModInt a = exp(y/2ll);
		a *= a;
		if(y&1)a*=(*this);
		return a;
	}
	bool operator==(const ModInt& x)const{return val==x.val;}
	inline bool operator!=(const ModInt& x)const{return !(*this==x);}
	bool operator<(const ModInt& x)const{return val<x.val;}
	bool operator>(const ModInt& x)const{return val>x.val;}
	inline bool operator>=(const ModInt& x)const{return !(*this<x);}
	inline bool operator<=(const ModInt& x)const{return !(*this>x);}
	ModInt& operator+=(const ModInt& x){if((val+=x.val)>=MOD)val-=MOD;return *this;}
	ModInt& operator-=(const ModInt& x){if((val+=MOD-x.val)>=MOD)val-=MOD;return *this;}
	ModInt& operator*=(const ModInt& x){(val*=x.val)%=MOD;return *this;}
	ModInt operator+(const ModInt& x)const{return ModInt(*this)+=x;}
	ModInt operator-(const ModInt& x)const{return ModInt(*this)-=x;}
	ModInt operator*(const ModInt& x)const{return ModInt(*this)*=x;}
};
istream& operator>>(istream&i,ModInt&x){i>>x.val;return i;}
ostream& operator<<(ostream&o,const ModInt&x){o<<x.val;return o;}
int d;
int l[305];
int s;
ModInt dp[2][2][100000];
int main(){
	scanf("%d",&d);
	for(int i=0;i<d;i++)scanf("%d",&l[i]);
	scanf("%d",&s);
	dp[0][0][0]=ModInt(1);
	for(int i=0;i<d;i++){
		for(int j=0;j<=300*(i+1);j++){
			dp[(i+1)%2][0][j]=dp[i%2][0][j];
			dp[(i+1)%2][1][j]=dp[i%2][1][j];
			if(j>=l[i])dp[(i+1)%2][1][j]+=dp[i%2][0][j-l[i]];
			if(j>=l[i])dp[(i+1)%2][0][j]+=dp[i%2][1][j-l[i]];
		}
	}
	ModInt ans;
	for(int i=0;i<=s;i++){
		ModInt a = ModInt(s-i);
		ans += a.exp((ll)d)*dp[d%2][0][i];
		ans -= a.exp((ll)d)*dp[d%2][1][i];
	}
	cout << ans << endl;
	return 0;
}