// 求组合数 package main import ( "bufio" "fmt" "os" ) var E *Enumeration func init() { const SIZE int = 1e6 + 10 const MOD int = 1e9 + 7 E = NewEnumeration(SIZE, MOD) } type Enumeration struct { fac, ifac, inv []int mod int } // 模数为质数时的组合数计算. func NewEnumeration(initSize, mod int) *Enumeration { res := &Enumeration{ fac: make([]int, 1, initSize+1), ifac: make([]int, 1, initSize+1), inv: make([]int, 1, initSize+1), mod: mod, } res.fac[0] = 1 res.ifac[0] = 1 res.inv[0] = 1 res.expand(initSize) return res } // 阶乘. func (e *Enumeration) Fac(k int) int { e.expand(k) return e.fac[k] } // 阶乘逆元. func (e *Enumeration) Ifac(k int) int { e.expand(k) return e.ifac[k] } // 模逆元. func (e *Enumeration) Inv(k int) int { e.expand(k) return e.inv[k] } // 组合数. func (e *Enumeration) C(n, k int) int { if n < 0 || k < 0 || n < k { return 0 } mod := e.mod return e.Fac(n) * e.Ifac(k) % mod * e.Ifac(n-k) % mod } // 排列数. func (e *Enumeration) P(n, k int) int { if n < 0 || k < 0 || n < k { return 0 } mod := e.mod return e.Fac(n) * e.Ifac(n-k) % mod } // 可重复选取元素的组合数. func (e *Enumeration) H(n, k int) int { if n == 0 { if k == 0 { return 1 } return 0 } return e.C(n+k-1, k) } // n个相同的球放入k个不同的盒子(盒子可放任意个球)的方法数. func (e *Enumeration) Put(n, k int) int { return e.C(n+k-1, n) } // 卡特兰数. func (e *Enumeration) Catalan(n int) int { return e.C(2*n, n) * e.Inv(n+1) % e.mod } func (e *Enumeration) expand(size int) { if upper := e.mod - 1; size > upper { size = upper } if len(e.fac) < size+1 { mod := e.mod preSize := len(e.fac) diff := size + 1 - preSize e.fac = append(e.fac, make([]int, diff)...) e.ifac = append(e.ifac, make([]int, diff)...) e.inv = append(e.inv, make([]int, diff)...) for i := preSize; i < size+1; i++ { e.fac[i] = e.fac[i-1] * i % mod } e.ifac[size] = Pow(e.fac[size], mod-2, mod) // !modInv for i := size - 1; i >= preSize; i-- { e.ifac[i] = e.ifac[i+1] * (i + 1) % mod } for i := preSize; i < size+1; i++ { e.inv[i] = e.ifac[i] * e.fac[i-1] % mod } } } func Pow(base, exp, mod int) int { base %= mod res := 1 for ; exp > 0; exp >>= 1 { if exp&1 == 1 { res = res * base % mod } base = base * base % mod } return res } func main() { in := bufio.NewReader(os.Stdin) out := bufio.NewWriter(os.Stdout) defer out.Flush() var T int fmt.Fscan(in, &T) for ; T > 0; T-- { var s string fmt.Fscan(in, &s) op := s[0] inner := s[2 : len(s)-1] var n, k int fmt.Sscanf(inner, "%d,%d", &n, &k) switch op { case 'C': fmt.Fprintln(out, E.C(n, k)) case 'P': fmt.Fprintln(out, E.P(n, k)) case 'H': fmt.Fprintln(out, E.H(n, k)) } } }