Let's introduce some definitions that will be needed later.

Let prime(x) be the set of prime divisors of x. For example, prime(140) = \{ 2, 5, 7 \}, prime(169) = \{ 13 \}.

Let g(x, p) be the maximum possible integer p^k where k is an integer such that x is divisible by p^k. For example:

  * g(45, 3) = 9 (45 is divisible by 3^2=9 but not divisible by 3^3=27), 
  * g(63, 7) = 7 (63 is divisible by 7^1=7 but not divisible by 7^2=49). 



Let f(x, y) be the product of g(y, p) for all p in prime(x). For example:

  * f(30, 70) = g(70, 2) ⋅ g(70, 3) ⋅ g(70, 5) = 2^1 ⋅ 3^0 ⋅ 5^1 = 10, 
  * f(525, 63) = g(63, 3) ⋅ g(63, 5) ⋅ g(63, 7) = 3^2 ⋅ 5^0 ⋅ 7^1 = 63. 



You have integers x and n. Calculate f(x, 1) ⋅ f(x, 2) ⋅ … ⋅ f(x, n) mod{(10^{9} + 7)}.

Input

The only line contains integers x and n (2 ≤ x ≤ 10^{9}, 1 ≤ n ≤ 10^{18}) — the numbers used in formula.

Output

Print the answer.

Examples

Input


10 2


Output


2


Input


20190929 1605


Output


363165664


Input


947 987654321987654321


Output


593574252

Note

In the first example, f(10, 1) = g(1, 2) ⋅ g(1, 5) = 1, f(10, 2) = g(2, 2) ⋅ g(2, 5) = 2.

In the second example, actual value of formula is approximately 1.597 ⋅ 10^{171}. Make sure you print the answer modulo (10^{9} + 7).

In the third example, be careful about overflow issue.
import sys
read=sys.stdin.buffer.readline
x,n=map(int,read().split())
i=2
fac=[]
while i*i<=x:
    if x%i==0:
        fac.append(i)
        while x%i==0:
            x//=i
    i+=1
if x>1:
    fac.append(x)

ans=[]
for el in fac:
    ct,z=0,1
    prd=el
    while prd<=n:
        d=n//prd
        ct+=z*d
        ct-=d*(z-1)
        z+=1
        prd*=el
    ans.append(ct)
md=1000000007
ct=1
#print(fac,ans)
for i in range(len(fac)):
    ct*=pow(fac[i],ans[i],md)
    ct%=md
print(ct)





'''
a=list(map(int,read().split()))
na=[]
for i in range(m):
    na.append([a[i],i])
na.sort(key=lambda x:x[0])
print(na)
ans=[0]*m
start,end=0,n-na[-1][0]+2
si,ei=0,m-1
fe=[0]*(m+1)
le=na[-1][0]
for i in range(m-1,-1,-1):
    if le==na[i][0]:
        end-=1
    fe[i]=end
print(fe)
flag=True
for i in range(m):
    start+=1
    if na[i][0]+start>=fe[i+1]:
        if i+1<m:
            if na[i+1][0]!=na[i][0]:
                ans[i]=fe[i+1]
            else:
                ans[i]=fe[i+1]-1
                if i>0 and ans[i]==ans[i-1]:
                    flag=False
        else:
            if na[i][0]+start-1<n:
                flag=False
            else:
                ans[i]=start
        ans[i+1:]=fe[i+1:m]
        break
    else:
        ans[i]=start
        start+=na[i][0]-1
if flag:
    print(ans)
else:
    print(-1)
'''