#include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios() { cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define FOR(i, begin, end) for (int i = (begin), i##_end_ = (end); i < i##_end_; i++) #define IFOR(i, begin, end) for (int i = (end)-1, i##_begin_ = (begin); i >= i##_begin_; i--) #define REP(i, n) FOR(i, 0, n) #define IREP(i, n) IFOR(i, 0, n) #define ALL(x) (x).begin(), (x).end() // template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T& m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T& m, const T q) { return m > q ? (m = q, true) : false; } template pair operator+(const pair& l, const pair& r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair& l, const pair& r) { return make_pair(l.first - r.first, l.second - r.second); } template vector srtunq(vector vec) { return sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()), vec; } template istream& operator>>(istream& is, vector& vec) { return for_each(begin(vec), end(vec), [&](T& v) { is >> v; }), is; } // output template ostream& dmpseq(ostream&, const T&, const string&, const string&, const string&); #if __cplusplus >= 201703L template ostream& operator<<(ostream& os, const tuple& tpl) { return apply([&os](auto&&... args) { ((os << args << ','), ...); }, tpl), os; } #endif // template ostream& operator<<(ostream& os, const pair& p) { return os << '(' << p.first << ',' << p.second << ')'; } template ostream& operator<<(ostream& os, const vector& x) { return dmpseq, T>(os, x, "[", ",", "]"); } template ostream& operator<<(ostream& os, const deque& x) { return dmpseq, T>(os, x, "deq[", ",", "]"); } template ostream& operator<<(ostream& os, const set& x) { return dmpseq, T>(os, x, "{", ",", "}"); } template ostream& operator<<(ostream& os, const unordered_set& x) { return dmpseq, T>(os, x, "{", ",", "}"); } template ostream& operator<<(ostream& os, const multiset& x) { return dmpseq, T>(os, x, "{", ",", "}"); } template ostream& operator<<(ostream& os, const map& x) { return dmpseq, pair>(os, x, "{", ",", "}"); } template ostream& operator<<(ostream& os, const unordered_map& x) { return dmpseq, pair>(os, x, "{", ",", "}"); } template ostream& dmpseq(ostream& os, const T& seq, const string& pre, const string& sp, const string& suf) { return os << pre, for_each(begin(seq), end(seq), [&](V x) { os << x << sp; }), os << suf; } template void print(const vector& x) { dmpseq, T>(cout, x, "", " ", "\n"); } #ifdef HITONANODE_LOCAL #define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl #else #define dbg(x) {} #endif template struct ModInt { using lint = long long; static int get_mod() { return mod; } static int get_primitive_root() { static int primitive_root = 0; if (!primitive_root) { primitive_root = [&](){ std::set fac; int v = mod - 1; for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i; if (v > 1) fac.insert(v); for (int g = 1; g < mod; g++) { bool ok = true; for (auto i : fac) if (ModInt(g).power((mod - 1) / i) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } int val; constexpr ModInt() : val(0) {} constexpr ModInt &_setval(lint v) { val = (v >= mod ? v - mod : v); return *this; } constexpr ModInt(lint v) { _setval(v % mod + mod); } explicit operator bool() const { return val != 0; } constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); } constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); } constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); } constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); } constexpr ModInt operator-() const { return ModInt()._setval(mod - val); } constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; } constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; } constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; } constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; } friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); } friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); } friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); } friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); } constexpr bool operator==(const ModInt &x) const { return val == x.val; } constexpr bool operator!=(const ModInt &x) const { return val != x.val; } bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; } friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val; return os; } constexpr lint power(lint n) const { lint ans = 1, tmp = this->val; while (n) { if (n & 1) ans = ans * tmp % mod; tmp = tmp * tmp % mod; n /= 2; } return ans; } constexpr lint inv() const { return this->power(mod - 2); } constexpr ModInt operator^(lint n) const { return ModInt(this->power(n)); } constexpr ModInt &operator^=(lint n) { return *this = *this ^ n; } inline ModInt fac() const { static std::vector facs; int l0 = facs.size(); if (l0 > this->val) return facs[this->val]; facs.resize(this->val + 1); for (int i = l0; i <= this->val; i++) facs[i] = (i == 0 ? ModInt(1) : facs[i - 1] * ModInt(i)); return facs[this->val]; } ModInt doublefac() const { lint k = (this->val + 1) / 2; if (this->val & 1) return ModInt(k * 2).fac() / ModInt(2).power(k) / ModInt(k).fac(); else return ModInt(k).fac() * ModInt(2).power(k); } ModInt nCr(const ModInt &r) const { if (this->val < r.val) return ModInt(0); return this->fac() / ((*this - r).fac() * r.fac()); } ModInt sqrt() const { if (val == 0) return 0; if (mod == 2) return val; if (power((mod - 1) / 2) != 1) return 0; ModInt b = 1; while (b.power((mod - 1) / 2) == 1) b += 1; int e = 0, m = mod - 1; while (m % 2 == 0) m >>= 1, e++; ModInt x = power((m - 1) / 2), y = (*this) * x * x; x *= (*this); ModInt z = b.power(m); while (y != 1) { int j = 0; ModInt t = y; while (t != 1) j++, t *= t; z = z.power(1LL << (e - j - 1)); x *= z, z *= z, y *= z; e = j; } return ModInt(std::min(x.val, mod - x.val)); } }; using mint = ModInt<1000000007>; int main() { int N, K; cin >> N >> K; const int B = N * 100; vector dp(B * 2 + 1); dp[B] = 1; while (N--) { int a; cin >> a; a -= K; vector nxt = dp; REP(i, dp.size()) { if (i + a < nxt.size()) nxt[i + a] += dp[i]; } dp = nxt; } cout << accumulate(dp.begin() + B, dp.end(), mint(0)) - 1 << '\n'; }