#include using namespace std; typedef long long signed int LL; typedef long long unsigned int LU; #define incII(i, l, r) for(int i = (l) ; i <= (r); ++i) #define incID(i, l, r) for(int i = (l) ; i < (r); ++i) #define decII(i, l, r) for(int i = (r) ; i >= (l); --i) #define decID(i, l, r) for(int i = (r) - 1; i >= (l); --i) #define inc(i, n) incID(i, 0, n) #define inc1(i, n) incII(i, 1, n) #define dec(i, n) decID(i, 0, n) #define dec1(i, n) decII(i, 1, n) #define inII(v, l, r) ((l) <= (v) && (v) <= (r)) #define inID(v, l, r) ((l) <= (v) && (v) < (r)) #define PB push_back #define EB emplace_back #define MP make_pair #define FI first #define SE second #define ALL(v) v.begin(), v.end() #define RALL(v) v.rbegin(), v.rend() template bool setmin (T & a, T b) { if(b < a) { a = b; return true; } else { return false; } } template bool setmax (T & a, T b) { if(b > a) { a = b; return true; } else { return false; } } template bool setmineq(T & a, T b) { if(b <= a) { a = b; return true; } else { return false; } } template bool setmaxeq(T & a, T b) { if(b >= a) { a = b; return true; } else { return false; } } LL mo(LL a, LL b) { assert(b > 0); a %= b; if(a < 0) { a += b; } return a; } LL fl(LL a, LL b) { assert(b > 0); return (a > 0 ? a / b : (a - b + 1) / b); } LL ce(LL a, LL b) { assert(b > 0); return (a < 0 ? a / b : (a + b - 1) / b); } #define bit(b, i) (((b) >> (i)) & 1) #define BC __builtin_popcountll #define SC(T, v) static_cast(v) #define SI(v) SC(int, v.size()) #define SL(v) SC( LL, v.size()) #define RF(e, v) for(auto & e: v) #define ei else if #define UR assert(false) // ---- ---- template class ModInt { private: LL v = 0; public: ModInt() { } ModInt(LL vv) { setval(vv); } ModInt & setval(LL vv) { v = vv % M; if(v < 0) { v += M; } return (*this); } LL getval() const { return v; } ModInt & operator+=(const ModInt & b) { return setval(v + b.v); } ModInt & operator-=(const ModInt & b) { return setval(v - b.v); } ModInt & operator*=(const ModInt & b) { return setval(v * b.v); } ModInt & operator/=(const ModInt & b) { return setval(v * b.inv()); } ModInt & operator^=( LU b) { return setval(ex(v, b)); } ModInt operator+ ( ) const { return ModInt(+v); } ModInt operator- ( ) const { return ModInt(-v); } ModInt operator+ (const ModInt & b) const { return ModInt(v + b.v); } ModInt operator- (const ModInt & b) const { return ModInt(v - b.v); } ModInt operator* (const ModInt & b) const { return ModInt(v * b.v); } ModInt operator/ (const ModInt & b) const { return ModInt(v * b.inv()); } ModInt operator^ ( LU b) const { return ModInt(ex(v, b)); } LL inv() const { LL x = (ex_gcd(v, M).FI + M) % M; assert(v * x % M == 1); return x; } LL ex(LL a, LU b) const { LL D = 64, x[64], y = 1; inc(i, D) { if((b >> i) == 0) { D = i; break; } } inc(i, D) { x[i] = (i == 0 ? a : x[i - 1] * x[i - 1]) % M; } inc(i, D) { if((b >> i) & 1) { (y *= x[i]) %= M; } } return y; } pair ex_gcd(LL a, LL b) const { if(b == 0) { return MP(1, 0); } auto p = ex_gcd(b, a % b); return MP(p.SE, p.FI - (a / b) * p.SE); } }; template ModInt operator+(LL a, const ModInt & b) { return b + a; } template ModInt operator-(LL a, const ModInt & b) { return -b + a; } template ModInt operator*(LL a, const ModInt & b) { return b * a; } template ModInt operator/(LL a, const ModInt & b) { return a * b.inv(); } template istream & operator>>(istream & is, ModInt & b) { LL v; is >> v; b.setval(v); return is; } template ostream & operator<<(ostream & os, const ModInt & b) { return (os << b.getval()); } // ---- ---- typedef ModInt<1'000'000'007> MI; #define LB(v, x) distance(v.begin(), lower_bound(ALL(v), x)) #define UB(v, x) distance(v.begin(), upper_bound(ALL(v), x)) MI f[100001]; int main() { int n, k; cin >> n >> k; vector a(n); inc(i, n) { cin >> a[i]; } sort(ALL(a)); LL s = (k % 2 == 0 && count(ALL(a), k / 2) > 1 ? UB(a, k / 2) : LB(a, k / 2)); LL l = (n - s), m = (s - l) / 2; incII(i, 0, n) { f[i] = (i < 2 ? 1 : f[i - 1] + (2 * i - 2) * (2 * i - 3) * f[i - 2]); } MI ans = f[m]; decID(i, s, n) { LL u = UB(a, k - a[i]); if(i < u) { u--; } assert(u <= i); LL x = max(0LL, u - (n - (i + 1))); ans *= x; } cout << ans << endl; return 0; }