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;

#define rep(i,n) for(long long i = 0; i < (long long)(n); i++)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define mt make_tuple
#define mp make_pair
template<class T1, class T2> bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); }
template<class T1, class T2> bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

using ll = long long; using ld = long double; using vll = vector<ll>; using vvll = vector<vll>; using vld = vector<ld>; 
using vi = vector<int>; using vvi = vector<vi>;
vll conv(vi& v) { vll r(v.size()); rep(i, v.size()) r[i] = v[i]; return r; }
using P = pair<ll, ll>;

template <typename T, typename U> ostream &operator<<(ostream &o, const pair<T, U> &v) {  o << "(" << v.first << ", " << v.second << ")"; return o; }
template<size_t...> struct seq{}; template<size_t N, size_t... Is> struct gen_seq : gen_seq<N-1, N-1, Is...>{}; template<size_t... Is> struct gen_seq<0, Is...> : seq<Is...>{};
template<class Ch, class Tr, class Tuple, size_t... Is>
void print_tuple(basic_ostream<Ch,Tr>& os, Tuple const& t, seq<Is...>){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get<Is>(t)), 0)...}; }
template<class Ch, class Tr, class... Args> 
auto operator<<(basic_ostream<Ch, Tr>& os, tuple<Args...> const& t) -> basic_ostream<Ch, Tr>& { os << "("; print_tuple(os, t, gen_seq<sizeof...(Args)>()); return os << ")"; }
ostream &operator<<(ostream &o, const vvll &v) { rep(i, v.size()) { rep(j, v[i].size()) o << v[i][j] << " "; cout << endl; } return o; }
template <typename T> ostream &operator<<(ostream &o, const vector<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]";  return o; }
template <typename T>  ostream &operator<<(ostream &o, const set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U>  ostream &operator<<(ostream &o, const map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U>  ostream &operator<<(ostream &o, const unordered_map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]";  return o; }
void printbits(ll mask, ll n) { rep(i, n) { cout << !!(mask & (1ll << i)); } cout << endl; }
#define ldout fixed << setprecision(40) 

static const double EPS = 1e-14;
static const long long INF = 1e18;
static const long long mo = 1e9+7;

class Mod {
    public:
        int num;
        int mod;
        Mod() : Mod(0) {}
        Mod(long long int n) : Mod(n, 1000000007) {}
        Mod(long long int n, int m) { mod = m; num = (n % mod + mod) % mod;}
        Mod(const string &s){ long long int tmp = 0; for(auto &c:s) tmp = (c-'0'+tmp*10) % mod; num = tmp; }
        Mod(int n) : Mod(static_cast<long long int>(n)) {}
        operator int() { return num; }
        void setmod(const int mod) { this->mod = mod; }
};
istream &operator>>(istream &is, Mod &x) { long long int n; is >> n; x = n; return is; }
ostream &operator<<(ostream &o, const Mod &x) { o << x.num; return o; }
Mod operator+(const Mod a, const Mod b) { return Mod((a.num + b.num) % a.mod); }
Mod operator+(const long long int a, const Mod b) { return Mod(a) + b; }
Mod operator+(const Mod a, const long long int b) { return b + a; }
Mod operator++(Mod &a) { return a + Mod(1); }
Mod operator-(const Mod a, const Mod b) { return Mod((a.mod + a.num - b.num) % a.mod); }
Mod operator-(const long long int a, const Mod b) { return Mod(a) - b; }
Mod operator--(Mod &a) { return a - Mod(1); }
Mod operator*(const Mod a, const Mod b) { return Mod(((long long)a.num * b.num) % a.mod); }
Mod operator*(const long long int a, const Mod b) { return Mod(a)*b; }
Mod operator*(const Mod a, const long long int b) { return Mod(b)*a; }
Mod operator*(const Mod a, const int b) { return Mod(b)*a; }
Mod operator+=(Mod &a, const Mod b) { return a = a + b; }
Mod operator+=(long long int &a, const Mod b) { return a = a + b; }
Mod operator-=(Mod &a, const Mod b) { return a = a - b; }
Mod operator-=(long long int &a, const Mod b) { return a = a - b; }
Mod operator*=(Mod &a, const Mod b) { return a = a * b; }
Mod operator*=(long long int &a, const Mod b) { return a = a * b; }
Mod operator*=(Mod& a, const long long int &b) { return a = a * b; }
Mod factorial(const long long n) {
    if (n < 0) return 0;
    Mod ret = 1;
    for (int i = 1; i <= n; i++) {
        ret *= i;
    }
    return ret;
}
Mod operator^(const Mod a, const long long n) {
    if (n == 0) return Mod(1);
    Mod res = (a * a) ^ (n / 2);
    if (n % 2) res = res * a;
    return res;
}
Mod modpowsum(const Mod a, const long long b) {
    if (b == 0) return 0;
    if (b % 2 == 1) return modpowsum(a, b - 1) * a + Mod(1);
    Mod result = modpowsum(a, b / 2);
    return result * (a ^ (b / 2)) + result;
}


/*************************************/
// ??\??????mod????´???°??§???????????????????????????
/*************************************/
Mod inv(const Mod a) { return a ^ (a.mod - 2); }
Mod operator/(const Mod a, const Mod b) { assert(b.num != 0); return a * inv(b); }
Mod operator/(const long long int a, const Mod b) { assert(b.num != 0); return Mod(a) * inv(b); }
Mod operator/=(Mod &a, const Mod b) { assert(b.num != 0); return a = a * inv(b); }

// n!??¨1/n!???????????????????????????
// nCr?????????????¨????????????????????????????
//
// assert??§n????¶?????????????????????????????????¨????????????????????¨???
//
// O(n log mo)
vector<Mod> fact, rfact;
void constructFactorial(const long long n) {
    fact.resize(n);
    rfact.resize(n);
    fact[0] = rfact[0] = 1;
    for (int i = 1; i < n; i++) {
        fact[i] = fact[i-1] * i;
        rfact[i] = Mod(1) / fact[i];
    }
}

// O(1)
Mod nCr(const long long n, const long long r) {
//    assert(n < (long long)fact.size());
    if (n < 0 || r < 0) return 0;
    return fact[n] * rfact[r] * rfact[n-r];
}

// O(k log mo) 
Mod nCrWithoutConstruction(const long long n, const long long k) {
    if (n < 0) return 0;
    if (k < 0) return 0;
    Mod ret = 1;
    for (int i = 0; i < k; i++) {
        ret *= n - (Mod)i;
        ret /= Mod(i+1);
    }
    return ret;
}
// n*m????????¢????????????????????????????????´????????°
// O(1)
Mod nBm(const long long n, const long long m) {
    if (n < 0 || m < 0) return 0;
    return nCr(n + m, n);
}

ll d, r;
vll l;
static int dp[301][100000][2] = {};
Mod f(ll i, ll s, bool b) {
    if (dp[i][s][b] >= 0) return dp[i][s][b];
    if (s < 0) return 0;
    if (i == d) return dp[i][s][b] = (Mod(s) ^ d) * (b ? -1 : 1);
    return dp[i][s][b] = f(i+1, s, b) + f(i+1, s-l[i], !b);
}

int main(void) {
    cin.tie(0); ios::sync_with_stdio(false);
    cin >> d; l.resize(d);
    rep(i, l.size()) cin >> l[i];
    cin >> r;
    rep(i, 301) rep(j, 100000) rep(h, 2) dp[i][j][h] = -1;
    cout << f(0, r, 0) << endl;
}