import sys, time, random from collections import deque, Counter, defaultdict input = lambda: sys.stdin.readline().rstrip() ii = lambda: int(input()) mi = lambda: map(int, input().split()) li = lambda: list(mi()) from math import gcd def isprime(n): if n <= 2: return n == 2 if n % 2 == 0: return False s = 0 t = n - 1 while t % 2 == 0: s += 1 t //= 2 for a in [2,325,9375,28178,450775,9780504,1795265022]: if a >= n: break x = pow(a, t, n) if x == 1 or x == n - 1: continue for _ in range(s): x = (x * x) % n if x == n - 1: break if x == n - 1: continue return False return True def Pollad(N): if N % 2 == 0: return 2 if isprime(N): return N def f(x): return (x * x + 1) % N step = 0 while True: step += 1 x = step y = f(x) while True: p = gcd(y - x + N, N) if p == 0 or p == N: break if p != 1: return p x = f(x) y = f(f(y)) def Primefact(N): if N == 1: return [] q = [] q.append(N) ret = [] while q: now = q.pop() if now == 1: continue p = Pollad(now) if p == now: ret.append(p) else: q.append(p) q.append(now // p) return Counter(ret) from copy import deepcopy class Modulo_Matrix_Error(Exception): pass Mod = 10 ** 9 + 6 class Modulo_Matrix(): __slots__=("ele","row","col","size") #入力 def __init__(self,M): """ 行列 M の定義 M: 行列 ※ Mod: 法はグローバル変数から指定 """ self.ele=[[x%Mod for x in X] for X in M] R=len(M) if R!=0: C=len(M[0]) else: C=0 self.row=R self.col=C self.size=(R,C) #出力 def __str__(self): T="" (r,c)=self.size for i in range(r): U="[" for j in range(c): U+=str(self.ele[i][j])+" " T+=U[:-1]+"]\n" return "["+T[:-1]+"]" def __repr__(self): return str(self) #+,- def __pos__(self): return self def __neg__(self): return self.__scale__(-1) #加法 def __add__(self,other): M=self.ele; N=other.ele L=[[0]*self.col for _ in range(self.row)] for i in range(self.row): Li,Mi,Ni=L[i],M[i],N[i] for j in range(self.col): Li[j]=Mi[j]+Ni[j] return Modulo_Matrix(L) def __iadd__(self,other): M=self.ele; N=other.ele for i in range(self.row): Mi,Ni=M[i],N[i] for j in range(self.col): Mi[j]+=Ni[j] Mi[j]%=Mod return self #減法 def __sub__(self,other): M=self.ele; N=other.ele L=[[0]*self.col for _ in range(self.row)] for i in range(self.row): Li,Mi,Ni=L[i],M[i],N[i] for j in range(self.col): Li[j]=Mi[j]-Ni[j] return Modulo_Matrix(L) def __isub__(self,other): M=self.ele; N=other.ele for i in range(self.row): Mi,Ni=M[i],N[i] for j in range(self.col): Mi[j]-=Ni[j] Mi[j]%=Mod return self #乗法 def __mul__(self,other): if isinstance(other,Modulo_Matrix): if self.col!=other.row: raise Modulo_Matrix_Error("左側の列と右側の行が一致しません.({},{})".format(self.size,other.size)) M=self.ele; N=other.ele E=[[0]*other.col for _ in range(self.row)] for i in range(self.row): Ei,Mi=E[i],M[i] for k in range(self.col): m_ik,Nk=Mi[k],N[k] for j in range(other.col): Ei[j]+=m_ik*Nk[j] Ei[j]%=Mod return Modulo_Matrix(E) elif isinstance(other,int): return self.__scale__(other) def __rmul__(self,other): if isinstance(other,int): return self.__scale__(other) def Inverse(self): if self.row!=self.col: raise Modulo_Matrix_Error("正方行列ではありません.") M=self N=M.row R=[[int(i==j) for j in range(N)] for i in range(N)] T=deepcopy(M.ele) for j in range(N): if T[j][j]==0: for i in range(j+1,N): if T[i][j]: break else: raise Modulo_Matrix_Error("正則行列ではありません") T[j],T[i]=T[i],T[j] R[j],R[i]=R[i],R[j] Tj,Rj=T[j],R[j] inv=pow(Tj[j],Mod-2,Mod) for k in range(N): Tj[k]*=inv; Tj[k]%=Mod Rj[k]*=inv; Rj[k]%=Mod for i in range(N): if i==j: continue c=T[i][j] Ti,Ri=T[i],R[i] for k in range(N): Ti[k]-=Tj[k]*c; Ti[k]%=Mod Ri[k]-=Rj[k]*c; Ri[k]%=Mod return Modulo_Matrix(R) #スカラー倍 def __scale__(self,r): M=self.ele L=[[(r*M[i][j])%Mod for j in range(self.col)] for i in range(self.row)] return Modulo_Matrix(L) #累乗 def __pow__(self,n): if self.row!=self.col: raise Modulo_Matrix_Error("正方行列ではありません.") def __mat_mul(A,B,r,Mod): E=[[0]*r for _ in range(r)] for i in range(r): a=A[i]; e=E[i] for k in range(r): b=B[k] for j in range(r): e[j]+=a[k]*b[j] e[j]%=Mod return E def __mat_pow(A,n,r,Mod): if n==0: return [[1 if i==j else 0 for j in range(r)] for i in range(r)] else: return __mat_mul(__mat_pow(A,n-1,r,Mod),A,r,Mod) if n&1 else __mat_pow(__mat_mul(A,A,r,Mod),n>>1,r,Mod) S=__mat_pow(self.ele,abs(n),self.col,Mod) if n>=0: return Modulo_Matrix(S) else: return Modulo_Matrix(S).Inverse() #等号 def __eq__(self,other): A=self B=other if A.size!=B.size: return False for i in range(A.row): for j in range(A.col): if A.ele[i][j]!=B.ele[i][j]: return False return True #不等号 def __neq__(self,other): return not(self==other) #転置 def Transpose(self): self.col,self.row=self.row,self.col self.ele=list(map(list,zip(*self.ele))) #行基本変形 def Row_Reduce(self): M=self (R,C)=M.size T=[] for i in range(R): U=[] for j in range(C): U.append(M.ele[i][j]) T.append(U) I=0 for J in range(C): if T[I][J]==0: for i in range(I+1,R): if T[i][J]!=0: T[i],T[I]=T[I],T[i] break if T[I][J]!=0: u=T[I][J] u_inv=pow(u,Mod-2,Mod) for j in range(C): T[I][j]*=u_inv T[I][j]%=Mod for i in range(R): if i!=I: v=T[i][J] for j in range(C): T[i][j]-=v*T[I][j] T[i][j]%=Mod I+=1 if I==R: break return Modulo_Matrix(T) #列基本変形 def Column_Reduce(self): M=self (R,C)=M.size T=[] for i in range(R): U=[] for j in range(C): U.append(M.ele[i][j]) T.append(U) J=0 for I in range(R): if T[I][J]==0: for j in range(J+1,C): if T[I][j]!=0: for k in range(R): T[k][j],T[k][J]=T[k][J],T[k][j] break if T[I][J]!=0: u=T[I][J] u_inv=pow(u,Mod-2,Mod) for i in range(R): T[i][J]*=u_inv T[i][J]%=Mod for j in range(C): if j!=J: v=T[I][j] for i in range(R): T[i][j]-=v*T[i][J] T[i][j]%=Mod J+=1 if J==C: break return Modulo_Matrix(T) #行列の階数 def Rank(self): M=self.Row_Reduce() (R,C)=M.size T=M.ele S=0 for i in range(R): f=False for j in range(C): if T[i][j]!=0: f=True break if f: S+=1 else: break return S #行の結合 def Row_Union(self,other): return Modulo_Matrix(self.ele+other.ele,Mod) #列の結合 def Column_Union(self,other): E=[] for i in range(self.row): E.append(self.ele[i]+other.ele[i]) return Modulo_Matrix(E) def __getitem__(self,index): assert isinstance(index,tuple) and len(index)==2 return self.ele[index[0]][index[1]] def __setitem__(self,index,val): assert isinstance(index,tuple) and len(index)==2 self.ele[index[0]][index[1]]=val #================================================= mod = 10 ** 9 + 7 n, k = mi() while k > 0: now = n C = Primefact(now) S = set(C.keys()) S.discard(2) S.discard(3) if S: k -= 1 n = 1 for v, c in C.items(): n *= pow(v + 1, c) else: break if k == 0: ans = n % mod else: p = 0 while n % 2 == 0: p += 1 n //= 2 q = 0 while n % 3 == 0: q += 1 n //= 3 A = Modulo_Matrix([[0, 2], [1, 0]]) A = A**k A *= Modulo_Matrix([[p,], [q,]]) ans = pow(2, A[0,0], mod) * pow(3, A[1,0], mod) % mod print(ans)