#include using i64 = std::int64_t; using u64 = std::uint64_t; #define REP(i, n) for (int i = 0; i < (i64)(n); ++i) #define ALL(x) std::begin(x), std::end(x) #define SIZE(a) (int)((a).size()) template inline bool chmax(T &a, T b) { return a < b and ((a = std::move(b)), true); } template inline bool chmin(T &a, T b) { return a > b and ((a = std::move(b)), true); } template using V = std::vector; template std::vector make_vec(size_t n, T a) { return std::vector(n, a); } template auto make_vec(size_t n, Ts... ts) { return std::vector(n, make_vec(ts...)); } template std::istream &operator>>(std::istream &is, std::vector &a) { for (auto &x : a) is >> x; return is; } template std::ostream &pprint(const Container &a, std::string_view sep = " ", std::string_view ends = "\n", std::ostream *os = nullptr) { if (os == nullptr) os = &std::cout; auto b = std::begin(a), e = std::end(a); for (auto it = std::begin(a); it != e; ++it) { if (it != b) *os << sep; *os << *it; } return *os << ends; } template struct is_iterable : std::false_type {}; template struct is_iterable())), decltype(std::end(std::declval()))>> : std::true_type {}; template ::value && !std::is_same::value>> std::ostream &operator<<(std::ostream &os, const T &a) { return pprint(a, ", ", "", &(os << "{")) << "}"; } template std::ostream &operator<<(std::ostream &os, const std::pair &a) { return os << "(" << a.first << ", " << a.second << ")"; } #ifdef ENABLE_DEBUG template void pdebug(const T &value) { std::cerr << value; } template void pdebug(const T &value, const Ts &... args) { pdebug(value); std::cerr << ", "; pdebug(args...); } #define DEBUG(...) \ do { \ std::cerr << " \033[33m (L" << __LINE__ << ") "; \ std::cerr << #__VA_ARGS__ << ":\033[0m "; \ pdebug(__VA_ARGS__); \ std::cerr << std::endl; \ } while (0) #else #define pdebug(...) #define DEBUG(...) #endif // Extended Euclidean algorithm // Returns gcd(a,b). // x and y are set to satisfy `a*x + b*y == gcd(a,b)` long long ext_gcd(long long a, long long b, long long &x, long long &y) { if (b == 0) { x = 1; y = 0; return a; } long long d = ext_gcd(b, a % b, y, x); y -= a / b * x; return d; } template struct ModInt { constexpr ModInt(long long val = 0) : _v(0) { if (val < 0) { long long k = (abs(val) + M - 1) / M; val += k * M; } assert(val >= 0); _v = val % M; } static constexpr int mod() { return M; } static constexpr unsigned int umod() { return M; } inline unsigned int val() const { return _v; } ModInt &operator++() { _v++; if (_v == umod()) _v = 0; return *this; } ModInt &operator--() { if (_v == 0) _v = umod(); _v--; return *this; } ModInt operator++(int) { auto result = *this; ++*this; return result; } ModInt operator--(int) { auto result = *this; --*this; return result; } constexpr ModInt operator-() const { return ModInt(-_v); } constexpr ModInt &operator+=(const ModInt &a) { if ((_v += a._v) >= M) _v -= M; return *this; } constexpr ModInt &operator-=(const ModInt &a) { if ((_v += M - a._v) >= M) _v -= M; return *this; } constexpr ModInt &operator*=(const ModInt &a) { _v = ((unsigned long long)(_v)*a._v) % M; return *this; } constexpr ModInt pow(unsigned long long t) const { assert(t >= 0); ModInt base = *this; ModInt res = 1; while (t) { if (t & 1) res *= base; base *= base; t >>= 1; } return res; } // Inverse by Extended Euclidean algorithm. // M doesn't need to be prime, but x and M must be coprime. constexpr ModInt inv() const { assert(_v != 0); long long x, y; long long g = ext_gcd(_v, M, x, y); assert(g == 1LL); // gcd(_v, M) must be 1. return x; } constexpr ModInt &operator/=(const ModInt &a) { return *this *= a.inv(); } friend constexpr ModInt operator+(const ModInt &a, const ModInt &b) { return ModInt(a) += b; } friend constexpr ModInt operator-(const ModInt &a, const ModInt &b) { return ModInt(a) -= b; } friend constexpr ModInt operator*(const ModInt &a, const ModInt &b) { return ModInt(a) *= b; } friend constexpr ModInt operator/(const ModInt &a, const ModInt &b) { return ModInt(a) /= b; } friend constexpr bool operator==(const ModInt &a, const ModInt &b) { return a._v == b._v; } friend constexpr bool operator!=(const ModInt &a, const ModInt &b) { return a._v != b._v; } friend std::istream &operator>>(std::istream &is, ModInt &a) { return is >> a._v; } friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a._v; } private: unsigned int _v; }; const unsigned int MOD = 1'000'000'007; using Mint = ModInt; // Runtime MOD: // unsigned int MOD = 1'000'000'007; // modifiable. // template struct ModInt { ... }; // using Mint = ModInt; using namespace std; int main() { cin.tie(nullptr); ios::sync_with_stdio(false); int N, K; cin >> N >> K; V A(N); cin >> A; // sort(A.rbegin(), A.rend()); const int M = (*max_element(ALL(A))) * N; auto dp = make_vec(N + 1, N + 1, M + 1, Mint(0)); dp[0][0][0] = 1; for (int i = 1; i <= N; ++i) { auto ai = A[i - 1]; dp[i][0][0] = 1; for (int j = 1; j <= i; ++j) { dp[i][j] = dp[i - 1][j]; for (int x = 0; x + ai <= M; ++x) { dp[i][j][x + ai] += dp[i - 1][j - 1][x]; } } } // if (N == 2 and K == 2) { // for (int j = 0; j <= N; ++j) { // for (int x = 0; x <= M; ++x) { // cerr << dp[N][j][x] << ' '; // } // cerr << endl; // } // } Mint ans = 0; REP(j, N + 1) { for (int x = j * K; x <= M; ++x) { ans += dp[N][j][x]; // if (dp[N][j][x].val() > 0) { // DEBUG(j, x, dp[N][j][x], ans.val()); // } } } cout << ans - 1 << endl; }