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.
#### IMPORTANT LIBRARY ####
 
############################
### DO NOT USE import random --> 250ms to load the library
############################
 
### In case of extra libraries: https://github.com/cheran-senthil/PyRival
 
######################
####### IMPORT #######
######################
 
from functools import cmp_to_key 
from collections import deque, Counter
from heapq import heappush, heappop
from math import log, ceil
 
######################
#### STANDARD I/O ####
######################
 
import sys
import os
from io import BytesIO, IOBase
 
BUFSIZE = 8192
 
class FastIO(IOBase):
    newlines = 0
    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None
 
    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()
 
    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()
 
    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)
 
class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")
 
if sys.version_info[0] < 3:
    sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
else:
    sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
 
def print(*args, **kwargs):
    sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop("end", "\n"))
    if kwargs.pop("flush", False):
        file.flush()
 
def inp():
    return sys.stdin.readline().rstrip("\r\n")  # for fast input
    
def ii():
    return int(inp())
 
def si():
    return str(inp())
 
def li(lag = 0):
    l = list(map(int, inp().split()))
    if lag != 0:
        for i in range(len(l)):
            l[i] += lag
    return l
    
def mi(lag = 0):
    matrix = list()
    for i in range(n):
        matrix.append(li(lag))
    return matrix
 
def lsi(): #string list
    return list(map(str, inp().split()))
 
def print_list(lista, space = " "):
    print(space.join(map(str, lista)))
 
######################
### BISECT METHODS ###
######################
 
def bisect_left(a, x):
    """i tale che a[i] >= x e a[i-1] < x"""
    left = 0
    right = len(a)
    while left < right:
        mid = (left+right)//2
        if a[mid] < x: 
            left = mid+1
        else: 
            right = mid
    return left
 
def bisect_right(a, x):
    """i tale che a[i] > x e a[i-1] <= x"""
    left = 0
    right = len(a)
    while left < right:
        mid = (left+right)//2
        if a[mid] > x: 
            right = mid
        else: 
            left = mid+1
    return left
 
def bisect_elements(a, x):
    """elementi pari a x nell'árray sortato"""
    return bisect_right(a, x) - bisect_left(a, x)
 
######################
### MOD OPERATION ####
######################
 
MOD = 10**9 + 7
maxN = 5
FACT = [0] * maxN
INV_FACT = [0] * maxN
 
def add(x, y):
    return (x+y) % MOD
   
def multiply(x, y):
    return (x*y) % MOD
 
def power(x, y):
    if y == 0:
        return 1
    elif y % 2:
        return multiply(x, power(x, y-1))
    else:
        a = power(x, y//2)
        return multiply(a, a)
 
def inverse(x):
    return power(x, MOD-2)
   
def divide(x, y):
    return multiply(x, inverse(y))
 
def allFactorials():
    FACT[0] = 1
    for i in range(1, maxN):
        FACT[i] = multiply(i, FACT[i-1])
 
def inverseFactorials():
    n = len(INV_FACT)
    INV_FACT[n-1] = inverse(FACT[n-1])
    for i in range(n-2, -1, -1):
        INV_FACT[i] = multiply(INV_FACT[i+1], i+1)
 
def coeffBinom(n, k):
    if n < k:
        return 0
    return multiply(FACT[n], multiply(INV_FACT[k], INV_FACT[n-k]))
 
######################
#### GRAPH ALGOS #####
######################
 
# ZERO BASED GRAPH
def create_graph(n, m, undirected = 1, unweighted = 1):
    graph = [[] for i in range(n)]
    if unweighted:
        for i in range(m):
            [x, y] = li(lag = -1)
            graph[x].append(y)
            if undirected:
                graph[y].append(x)
    else:
        for i in range(m):
            [x, y, w] = li(lag = -1)
            w += 1
            graph[x].append([y,w])
            if undirected:
                graph[y].append([x,w])
    return graph
 
def create_tree(n, unweighted = 1):
    children = [[] for i in range(n)]
    if unweighted:
        for i in range(n-1):
            [x, y] = li(lag = -1)
            children[x].append(y)
            children[y].append(x)
    else:
        for i in range(n-1):
            [x, y, w] = li(lag = -1)
            w += 1
            children[x].append([y, w])
            children[y].append([x, w])
    return children
   
def dist(tree, n, A, B = -1):
    s = [[A, 0]]
    massimo, massimo_nodo = 0, 0
    distanza = -1
    v = [-1] * n
    while s:
        el, dis = s.pop() 
        if dis > massimo:
            massimo = dis
            massimo_nodo = el
        if el == B:
            distanza = dis
        for child in tree[el]:
            if v[child] == -1:
                v[child] = 1
                s.append([child, dis+1])
    return massimo, massimo_nodo, distanza
 
def diameter(tree):
    _, foglia, _ = dist(tree, n, 0)
    diam, _, _ = dist(tree, n, foglia)
    return diam
   
def dfs(graph, n, A):
    v = [-1] * n
    s = [[A, 0]]
    v[A] = 0
    while s:
        el, dis = s.pop()
        for child in graph[el]:
            if v[child] == -1:
                v[child] = dis + 1
                s.append([child, dis + 1])
    return v #visited: -1 if not visited, otherwise v[B] is the distance in terms of edges
 
def bfs(graph, n, A):
    v = [-1] * n
    s = deque()
    s.append([A, 0])
    v[A] = 0
    while s:
        el, dis = s.popleft()
        for child in graph[el]:
            if v[child] == -1:
                v[child] = dis + 1
                s.append([child, dis + 1])
    return v #visited: -1 if not visited, otherwise v[B] is the distance in terms of edges
 
#FROM A GIVEN ROOT, RECOVER THE STRUCTURE
def parents_children_root_unrooted_tree(tree, n, root = 0):
    q = deque()
    visited = [0] * n
    parent = [-1] * n
    children = [[] for i in range(n)]
    q.append(root)
    while q:
        all_done = 1
        visited[q[0]] = 1
        for child in tree[q[0]]:
            if not visited[child]:
                all_done = 0
                q.appendleft(child)
        if all_done:
            for child in tree[q[0]]:   
                if parent[child] == -1:
                    parent[q[0]] = child
                    children[child].append(q[0])
            q.popleft()
    return parent, children
 
# CALCULATING LONGEST PATH FOR ALL THE NODES 
def all_longest_path_passing_from_node(parent, children, n):
    q = deque()
    visited = [len(children[i]) for i in range(n)]
    downwards = [[0,0] for i in range(n)]
    upward = [1] * n
    longest_path = [1] * n
    for i in range(n):
        if not visited[i]:
            q.append(i)
            downwards[i] = [1,0]
    while q:
        node = q.popleft()
        if parent[node] != -1:
            visited[parent[node]] -= 1
            if not visited[parent[node]]:
                q.append(parent[node])
        else:
            root = node
        for child in children[node]:   
            downwards[node] = sorted([downwards[node][0], downwards[node][1], downwards[child][0] + 1], reverse = True)[0:2]
    s = [node]
    while s:
        node = s.pop()
        if parent[node] != -1:
            if downwards[parent[node]][0] == downwards[node][0] + 1:
                upward[node] = 1 + max(upward[parent[node]], downwards[parent[node]][1])
            else:
                upward[node] = 1 + max(upward[parent[node]], downwards[parent[node]][0])
        longest_path[node] = downwards[node][0] + downwards[node][1] + upward[node] - min([downwards[node][0], downwards[node][1], upward[node]]) - 1
        for child in children[node]:
            s.append(child)
    return longest_path
 
### TBD SUCCESSOR GRAPH 7.5
### TBD TREE QUERIES 10.2 da 2 a 4
### TBD ADVANCED TREE 10.3
### TBD GRAPHS AND MATRICES 11.3.3 e 11.4.3 e 11.5.3 (ON GAMES)
 
######################
## END OF LIBRARIES ##
######################

"""
def tree_levels(root):
    queue = deque()
    queue.append([root,1])
    visited = [0 for i in range(n)]
    visited[root] = 1
    level = [0 for i in range(n)]
    while queue:
        node, lev = queue.popleft()
        level[node] = lev
        for ch in tree[node]:
            if visited[ch] == 0:
                visited[ch] = 1
                queue.append([ch, lev+1])
    return level
 
MAX_ESP = 14
def pow2_ancestors(root):
    res = [[-1 for i in range(MAX_ESP)] for j in range(n)] 
    visited = [0 for i in range(n)]
    queue = deque()
    queue.append(root)
    visited[root] = 1
    while queue:
        par = queue.popleft()
        for ch in tree[par]:
            if visited[ch] == 0:
                visited[ch] = 1
                res[ch][0] = par
                queue.append(ch)
    for esp in range(1,MAX_ESP):
        for i in range(n):
            interm_par = res[i][esp-1]
            if interm_par != -1:
                res[i][esp] = res[interm_par][esp-1]
    return res
    
def kth_ancestor(root,node,k):
    pow2 = pow2_ancestors(root)
    esp = 0
    curr_par = node
    while k:
        if k % 2 == 1:
            interm_par = pow2[curr_par][esp]
            curr_par = interm_par
        esp += 1
        k = k >> 1
    print(curr_par)

def lowest_common_ancestor(root,a,b):
    dist_ab = 0
    if levels[a] < levels[b]:
        a,b = b,a
    for i in range(MAX_ESP-1,-1,-1):
        if levels[a]-2**i >= levels[b]:
            a = pow2[a][i]
            dist_ab += 2**i
    if a == b:
        return a, dist_ab
    for i in range(MAX_ESP-1,-1,-1):
        if pow2[a][i] != pow2[b][i]:
            a = pow2[a][i]
            b = pow2[b][i]
            dist_ab += 2**(i+1)
    return pow2[a][0], dist_ab+2
    
def calcola(a,x):
    if n*a+x not in memo and n*x+a not in memo:
        _,d_ax = lowest_common_ancestor(root,a,x)
        memo[n*a+x] = d_ax
    elif n*a+x in memo:
        d_ax = memo[n*a+x]
    else:
        d_ax = memo[n*x+a]
    return d_ax
    
n = ii()
tree = create_tree(n)
root = 0
levels = tree_levels(root)
pow2 = pow2_ancestors(root)
q = ii()
memo = dict()
for query in range(q):
    x,y,a,b,k = li(lag = -1)
    figli = (x in tree[y]) or (y in tree[x])
    k += 1
    d_ab = calcola(a,b)
    if (d_ab % 2) == (k % 2) and d_ab <= k:
        print("YES")
    elif figli == True:
        print("NO")
    else:
        d_ax = calcola(a,x)
        d_by = calcola(b,y)
        d1 = d_ax+d_by+1
        if (d1 % 2) == (k % 2) and d1 <= k:
            print("YES")
        else:
            d_ay = calcola(a,y)
            d_bx = calcola(b,x)
            d2 = d_ay+d_bx+1  
            if (d2 % 2) == (k % 2) and d2 <= k:
                print("YES")
            else:
                print("NO")
"""

from collections import Counter


def gcd(x, y):
    """greatest common divisor of x and y"""
    while y:
        x, y = y, x % y
    return x


def memodict(f):
    """memoization decorator for a function taking a single argument"""
    class memodict(dict):
        def __missing__(self, key):
            ret = self[key] = f(key)
            return ret

    return memodict().__getitem__


def pollard_rho(n):
    """returns a random factor of n"""
    if n & 1 == 0:
        return 2
    if n % 3 == 0:
        return 3

    s = ((n - 1) & (1 - n)).bit_length() - 1
    d = n >> s
    for a in [2, 325, 9375, 28178, 450775, 9780504, 1795265022]:
        p = pow(a, d, n)
        if p == 1 or p == n - 1 or a % n == 0:
            continue
        for _ in range(s):
            prev = p
            p = (p * p) % n
            if p == 1:
                return gcd(prev - 1, n)
            if p == n - 1:
                break
        else:
            for i in range(2, n):
                x, y = i, (i * i + 1) % n
                f = gcd(abs(x - y), n)
                while f == 1:
                    x, y = (x * x + 1) % n, (y * y + 1) % n
                    y = (y * y + 1) % n
                    f = gcd(abs(x - y), n)
                if f != n:
                    return f
    return n


@memodict
def prime_factors(n):
    """returns a Counter of the prime factorization of n"""
    if n <= 1:
        return Counter()
    f = pollard_rho(n)
    return Counter([n]) if f == n else prime_factors(f) + prime_factors(n // f)
    

x,n = li()
primi = prime_factors(x)
res = 1
for p in primi:
    e = 0
    i = 1
    while p**i <= n:
        e += n//p**i
        i += 1
    res = multiply(res, power(p, e))
print(res)

    
    
    
    