import io import sys _INPUT = """\ 6 2 2 6 3 1 2 102 97 """ def gcd(a, b): while b: a, b = b, a % b return a def lcm(a, b): return a // gcd(a, b) * b def isPrimeMR(n): d = n - 1 d = d // (d & -d) L = [2, 7, 61] if n < 1<<32 else [2, 3, 5, 7, 11, 13, 17] if n < 1<<48 else [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37] for a in L: t = d y = pow(a, t, n) if y == 1: continue while y != n - 1: y = y * y % n if y == 1 or t == n - 1: return 0 t <<= 1 return 1 def findFactorRho(n): m = 1 << n.bit_length() // 8 for c in range(1, 99): f = lambda x: (x * x + c) % n y, r, q, g = 2, 1, 1, 1 while g == 1: x = y for i in range(r): y = f(y) k = 0 while k < r and g == 1: ys = y for i in range(min(m, r - k)): y = f(y) q = q * abs(x - y) % n g = gcd(q, n) k += m r <<= 1 if g == n: g = 1 while g == 1: ys = f(ys) g = gcd(abs(x - ys), n) if g < n: if isPrimeMR(g): return g elif isPrimeMR(n // g): return n // g return findFactorRho(g) def primeFactor(n): i = 2 ret = {} rhoFlg = 0 while i * i <= n: k = 0 while n % i == 0: n //= i k += 1 if k: ret[i] = k i += i % 2 + (3 if i % 3 == 1 else 1) if i == 101 and n >= 2 ** 20: while n > 1: if isPrimeMR(n): ret[n], n = 1, 1 else: rhoFlg = 1 j = findFactorRho(n) k = 0 while n % j == 0: n //= j k += 1 ret[j] = k if n > 1: ret[n] = 1 if rhoFlg: ret = {x: ret[x] for x in sorted(ret)} return ret def divisors(N): pf = primeFactor(N) ret = [1] for p in pf: ret_prev = ret ret = [] for i in range(pf[p]+1): for r in ret_prev: ret.append(r * (p ** i)) return sorted(ret) def solve(test): def ExtGCD(a, b): if b: g, y, x = ExtGCD(b, a % b) y -= (a // b)*x return g, x, y return a, 1, 0 import math def Ch_Rem(b1,b2,m1,m2): g,p,q=ExtGCD(m1,m2) d=math.gcd(m1,m2) lcm=m1*m2//d return (b1+m1//d*(b2-b1)*p)%lcm N,P=map(int,input().split()) mod=10**9+7 # print(primeFactor(10**9+6)) tmp=0 for i in range(N): now=i+1 while now%P==0: tmp+=1 now//=P m=1 for i in range(N): m*=i+1 m%=mod n1=1 n2=1 for i in range(N): n1*=i+1 n2*=i+1 n1%=2 n2%=500000003 n=Ch_Rem(n1,n2,2,500000003) # print(n) ans=(pow(m,n,mod)*tmp)%mod if test==0: print(ans) else: return None def random_input(): from random import randint,shuffle N=randint(1,10) M=randint(1,N) A=list(range(1,M+1))+[randint(1,M) for _ in range(N-M)] shuffle(A) return (" ".join(map(str, [N,M]))+"\n"+" ".join(map(str, A))+"\n")*3 def simple_solve(): return [] def main(test): if test==0: solve(0) elif test==1: sys.stdin = io.StringIO(_INPUT) case_no=int(input()) for _ in range(case_no): solve(0) else: for i in range(1000): sys.stdin = io.StringIO(random_input()) x=solve(1) y=simple_solve() if x!=y: print(i,x,y) print(*[line for line in sys.stdin],sep='') break #0:提出用、1:与えられたテスト用、2:ストレステスト用 main(0)