Harryxun/sft_time huggingface dataset:
### BUGGY CODE ###

N = int(input())
A = list(map(int,input().split()))

def P(m):
    pf={}
    for i in range(2,int(m**0.5)+1):
        while m%i==0:
            pf[i]=pf.get(i,0)+1
            m//=i
    if m>1:
        pf[m]=1
    return pf

dictlist = []
for i in range(N):
    dictlist.append(P(A[i]))

dict = dictlist[0].copy()
for i in range(1,N):
    new = dictlist[i]
    for k in new.keys():
        if k not in dict:
            dict[k]=new[k]
        elif dict[k]<new[k]:
            dict[k]=new[k]

output = 0
for i in range(N):
    tdict = dict.copy()
    out = 1
    tmp = dictlist[i]
    for k in tmp.keys():
        tdict[k] = tdict[k]-tmp[k]
    for k in tdict.keys():
        out *= int(k)**tdict[k] %(10**9+7)
    output += out %(10**9+7)
    output = output % (10**9+7)
print(output)

### FIXED CODE ###

N = int(input())
A = list(map(int,input().split()))

import fractions

X = A[0]
for i in range(1, N):
    X = X*A[i] // fractions.gcd(X, A[i])

output = 0
D =10**9+7
X = X%D

for i in range(N):
    output += X*pow(A[i],D-2,D)%D
    output = output % (10**9+7)
print(int(output))
### BUGGY CODE ###

N,K = map(int,input().split())
p_list = list(map(int,input().split()))

# kitaichi_p_list = [(p + 1)/2 for p in p_list]

max_sum = 0
for i in range(N):
    tmp_sum = sum(p_list[i:i+K])
    if(max_sum < tmp_sum):
        max_sum = tmp_sum
        ichi = i

kitaichi = [(p+1)/2 for p in p_list[ichi:ichi+K]]

print(sum(kitaichi))

### FIXED CODE ###

from sys import stdin

def main():

    input = stdin.readline

    N,K = map(int,input().split())
    p_list = [(p+1)/2 for p in list(map(int,input().split()))]

    # Sを計算
    S = [0]
    for p in p_list:
        S.append(S[-1] + p)
        # print(S)

    # i:i+kを計算

    maxs = 0
    for i in range(N-K+1):
        p_num = S[i+K] - S[i]
        if(maxs < p_num):
            maxs = p_num
    
    print(maxs)

if __name__ == "__main__":
    main()
### BUGGY CODE ###

import sys
MAX_INT = int(10e10)
MIN_INT = -MAX_INT
mod = 1000000007
sys.setrecursionlimit(1000000)
def IL(): return list(map(int,input().split()))
def SL(): return input().split()
def I(): return int(sys.stdin.readline())
def S(): return input()

def init(n):
  for i in range(N):
    par[i]=i
    num[i]=0
def find(x):
  if par[x]==x:
    return x
  else:
    return find(par[x])
def unite(x,y):
  if (y<x):
    par[x]=y
  else:
    par[y]=x
def same(x,y):
  return find(x)==find(y)
def cnt(x,tmp):
  res = tmp + num[x]
  if par[x]==x:
    return res
  else:
    return cnt(par[x],res)


N,Q = IL()
ab = [IL() for i in range(N-1)]
px = [IL() for i in range(Q)]

par=[0 for i in range(N+1)]
num=[0 for i in range(N+1)]

init(N)

for a,b in ab:
  unite(a,b)

for p,x in px:
  num[p] += x

ans = []
for i in range(1,N+1):
  ans.append(cnt(i,0))

print(" ".join(map(str,ans)))

### FIXED CODE ###

import sys
MAX_INT = int(10e10)
MIN_INT = -MAX_INT
mod = 1000000007
sys.setrecursionlimit(1000000)
def IL(): return list(map(int,input().split()))
def SL(): return input().split()
def I(): return int(sys.stdin.readline())
def S(): return input()

def init(n):
  for i in range(N):
    par[i]=i
    num[i]=0
def find(x):
  if par[x]==x:
    return x
  else:
    return find(par[x])
def unite(x,y):
  if (y<x):
    par[x]=y
  else:
    par[y]=x
def same(x,y):
  return find(x)==find(y)
def cnt(x):
  if par[x]==x:
    res = num[x]
    return res
  else:
    if used[par[x]] == True:
      res = num[x] + ans[par[x]]
      return res
    else:
      return

N,Q = IL()
ab = [IL() for i in range(N-1)]
px = [IL() for i in range(Q)]

par=[0 for i in range(N+1)]
num=[0 for i in range(N+1)]

init(N)

for a,b in ab:
  unite(a,b)

for p,x in px:
  num[p] += x

ans = [0 for i in range(N+1)]
used = [False for i in range(N+1)]
for i in range(1,N+1):
  ans[i] = cnt(i)
  used[i] = True

print(" ".join(map(str,ans[1:])))
### BUGGY CODE ###

from collections import deque
n,m=map(int,input().split())
g=[[] for i in range(n)]
for i in range(m):
    a,b=map(int,input().split())
    g[a-1].append(b-1)
gken=[[] for i in range(n)]
for i in range(n):
    for j in g[i]:
        for j2 in g[j]:
            for j3 in g[j2]:
                gken[i].append(j3)

s,t=map(int,input().split())
s-=1
t-=1
q=deque([[s,0]])
v=[0]*n
while q:
    p=q.popleft()
    v[p[0]]=1
    for j3 in gken[p[0]]:
        if j3==t:
            print(p[1]+1)
            exit()
        if v[j3]==0:
            v[j3]=1
            q.append([j3,p[1]+1])
print(-1)


### FIXED CODE ###

from collections import deque
n,m=map(int,input().split())
g=[[] for i in range(3*n)]
for i in range(m):
    a,b=map(int,input().split())
    g[3*(a-1)].append(3*(b-1)+1)
    g[3*(a-1)+1].append(3*(b-1)+2)
    g[3*(a-1)+2].append(3*(b-1))
s,t=map(int,input().split())
s-=1
t-=1
s*=3
t*=3
q=deque([[s,0]])
v=[0]*(3*n)
while q:
    p=q.popleft()
    v[p[0]]=1
    for j3 in g[p[0]]:
        if j3==t:
            print((p[1]+1)//3)
            exit()
        if v[j3]==0:
            v[j3]=1
            q.append([j3,p[1]+1])
print(-1)
### BUGGY CODE ###

n=int(input())
a=list(map(int,input().split()))
b=1
for i in range(n):
    b*=a[i]
print(b if b<=10**18 else -1)

### FIXED CODE ###

n=int(input())
a=list(map(int,input().split()))
b=1
if 0 in a:
    print(0)
    exit()
for i in range(n):
    b*=a[i]
    if b>10**18:
        print(-1)
        exit()
print(b)
### BUGGY CODE ###

from fractions import gcd
from functools import reduce

def gcd_list(numbers):
    return reduce(gcd, numbers)
  
def lcm_base(x, y):
    return (x * y) // gcd(x, y)

def lcm_list(numbers):
    return reduce(lcm_base, numbers, 1)
n, m = map(int, input().split())
A = list(map(lambda x: int(x)//2, input().split()))
g = gcd_list(A)
l = lcm_list(A)
if (l//g)%2 == 0:
  print(0)
else:
  print(((m//l)+1)//2)

### FIXED CODE ###

from fractions import gcd
from functools import reduce

def lcm(x, y):
  g = gcd(x, y)
  x //= g
  y //= g
  if x&y&1:
    l = x*y*g
    if l > 10**9:
      return 0
    return l
  return 0
n, m = map(int, input().split())
A = list(map(lambda x: int(x)//2, input().split()))
k = reduce(lcm, A)
if k == 0:
  print(0)
else:
  print(((m//k)+1)//2)
### BUGGY CODE ###

n,m = map(int,input().split())
dic = {}
for i in range(m):
  a,b = map(int,input().split())
  if a not in dic:
    dic[a]=[b]    
  else:    
    if b not in dic[a]:
      dic[a].append(b)      
      
  if b not in dic:
    dic[b]=[a]
    if a not in dic[b]:
      dic[b].append(a)
      
ans = 'IMPOSSIBLE'
for i in dic[1]:   
  if n in dic[i]:
    ans = 'POSSIBLE'
    break
    
print(ans)

### FIXED CODE ###

n,m = map(int,input().split())
dic = {i+1:set() for i in range(n)}
for i in range(m):
  a,b = map(int,input().split())
  dic[a].add(b)
  dic[b].add(a)
        
ans = 'IMPOSSIBLE'
for i in dic[1]:   
  if n in dic[i]:
    ans = 'POSSIBLE'
    break
    
print(ans)
### BUGGY CODE ###

import sys
import heapq as hq
input = sys.stdin.readline
N = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
for i in range(N):
  if b[i] == b[i - 1]:
    if a[i] == b[i] and (a[i - 1] == b[i - 1]): continue
    print(-1)
    exit(0)
base = 10 ** 10
sb = [-(b[i] * base + i) for i in range(N) if a[i] != b[i]]
hq.heapify(sb)
res = 0
while len(sb):
  #print(b, sb)
  v = hq.heappop(sb)
  i = -v % base
  if a[i] == b[i]: continue
  v2 = a[i]
  if len(sb):
    p = hq.heappop(sb)
    v2 = -p // base
    hq.heappush(sb, p)

  x = b[i - 1] + b[(i + 1) % N]
  if b[i] < x:
    print(-1)
    exit(0)
  res += -((v2 - b[i]) // x)
  b[i] -= -((v2 - b[i]) // x) * x
  if b[i] <= 0:
    print(-1)
    exit(0)
  if b[i] > a[i]:
    hq.heappush(sb, -(b[i] * base + i))
if a == b:
  print(res)
else: print(-1)

### FIXED CODE ###

import sys
from heapq import heappush as hpu
from heapq import heappop as hpo
input = sys.stdin.readline
N = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))

base = 10 ** 6
sb = [-(b[i] * base + i) for i in range(N) if a[i] != b[i]]
h = []
for t in sb: hpu(h, t)
res = 0
while len(h):
  v = hpo(h)
  i = -v % base
  v = -v // base
  if v < a[i]:
    print(-1)
    exit(0)
  d = v - a[i]
  x = b[i - 1] + b[(i + 1) % N]
  t = d // x
  if t == 0:
    if v == a[i]: continue
    print(-1)
    exit(0)
  b[i] -= x * (t)
  res += t
  hpu(h, -(b[i] * base + i))
print(res)
### BUGGY CODE ###

BIT = [0] * ((1 << 19) + 1)
def add(i, x):
    while i <= (1 << 19):
        BIT[i] += x
        i += i & (-i)
def query(i):
    res = 0
    while i > 0:
        res += BIT[i]
        i -= i & (-i)
    return res
n, q = map(int, input().split())
c = list(map(int, input().split()))
Q = [[] for i in range(n)]
for i in range(q):
    l, r = map(int, input().split())
    Q[r - 1].append([l - 1, i])
l = [-1] * n
a = [-1] * q
add(1, n)
for i in range(n):
    add(l[c[i] - 1] + 2, -1)
    add(i + 2, 1)
    l[c[i] - 1] = i
    for j in Q[i]:
        a[j[1]] = query(1 << 19) - query(j[0] + 1)
print(*a, sep="\n")

### FIXED CODE ###

BIT = [0] * ((1 << 19) + 1)
def add(i, x):
    while i <= (1 << 19):
        BIT[i] += x
        i += i & -i
def query(i):
    res = 0
    while i > 0:
        res += BIT[i]
        i -= i & -i
    return res
n, q = map(int, input().split())
c = list(map(int, input().split()))
Q = [[] for i in range(n)]
for i in range(q):
    l, r = map(int, input().split())
    Q[r - 1].append([l - 1, i])
l = [-1] * n
a = [-1] * q
add(1, n)
for i in range(n):
    add(l[c[i] - 1] + 2, -1)
    add(i + 2, 1)
    l[c[i] - 1] = i
    for j in Q[i]:
        a[j[1]] = query(1 << 19) - query(j[0] + 1)
print(*a, sep="\n")
### BUGGY CODE ###

from collections import deque
H, W = map(int, input().split())
maze = [input() for _ in range(H)]


def bfs(x, y):
    visited, queue = [], deque([(x, y, 0)])
    max_cost = 0
    while queue:
        px, py, cost = queue.popleft()
        max_cost = max(max_cost, cost)

        candidate = ((px + 1, py), (px - 1, py), (px, py + 1), (px, py - 1))
        visited.append((px, py))
        for cx, cy in candidate:
            if 0 <= cx < W and 0 <= cy < H and not (cx, cy) in visited and maze[cy][cx] == ".":
                queue.append((cx, cy, cost + 1))
    return max_cost


ans = 0
for y in range(H):
    for x in range(W):
        if maze[y][x] == ".":
            ans = max(ans, bfs(x, y))

print(ans)


### FIXED CODE ###

H, W = map(int, input().split())
m = [list(input()) for _ in range(H)]
inf = 10**3

V = H*W
maze = [[inf]*V for _ in range(V)]

for i in range(V):
    maze[i][i] = 0

for py in range(H):
    for px in range(W):
        if m[py][px] == "#":
            continue
        candidate = [(px+1, py), (px-1, py), (px, py+1), (px, py-1)]
        for x, y in candidate:
            if not (0<=x<W and 0<=y<H):continue
            if m[y][x] == "#":
                continue
            maze[W*py+px][W*y+x] = 1

for k in range(V):
    for i in range(V):
        for j in range(V):
            maze[i][j] = min(maze[i][j], maze[i][k]+maze[k][j])

print(max([j for i in maze for j in i if j!=inf]))
### BUGGY CODE ###

from heapq import heappush, heappop
import time
from decimal import *
stime=time.time()
sx,sy,gx,gy=map(int,input().split())
n=int(input())
g = [[] for i in range(n+2)]
data=[(sx+sy*1j,0)]
for i in range(n):
    a,b,c=map(int,input().split())
    data.append((a+b*1j,c))
data.append((gx+gy*1j,0))
getcontext().prec = 12
for i in range(n+2):
    for j in range(i+1,n+2):
        tmp=abs(data[i][0]-data[j][0])-data[i][1]-data[j][1]
        g[i].append((Decimal(tmp),j))
        g[j].append((Decimal(tmp),i))

dist=[Decimal(2828427127) for i in range(n+2)]
visited=[False for i in range(n+2)]
dist[0]=0
que=[]
heappush(que,(Decimal(0),0))

while que:
    if time.time()-stime>1.4:
        break
    c,v=heappop(que)
    if visited[v]:
        continue
    visited[v]=True
    for x in g[v]:
        if visited[x[1]]:
            continue
        tmp=x[0]+c if not x[0]<0 else c
        if tmp<dist[x[1]]:
            dist[x[1]]=tmp
            heappush(que,(tmp,x[1]))
print(dist[n+1])


### FIXED CODE ###

from heapq import heappush, heappop
sx,sy,gx,gy=map(int,input().split())
n=int(input())
g = [[] for i in range(n+2)]
data=[(sx+sy*1j,0)]
for i in range(n):
    a,b,c=map(int,input().split())
    data.append((a+b*1j,c))
data.append((gx+gy*1j,0))

for i in range(n+2):
    for j in range(i+1,n+2):
        tmp=abs(data[i][0]-data[j][0])-data[i][1]-data[j][1]
        g[i].append((tmp,j))
        g[j].append((tmp,i))

dist=[2828427127 for i in range(n+2)]
visited=[False for i in range(n+2)]
dist[0]=0
que=[]
heappush(que,(0,0))

while que:
    c,v=heappop(que)
    if visited[v]:
        continue
    visited[v]=True
    for x in g[v]:
        if visited[x[1]]:
            continue
        tmp=x[0]+c if not x[0]<0 else c
        if tmp<dist[x[1]]:
            dist[x[1]]=tmp
            heappush(que,(tmp,x[1]))
print(dist[n+1])
### BUGGY CODE ###


A, B, C, D = map(int, input().split())

CN = C
DN = D
while CN != DN:
    if CN < DN:
        CN += C
    else:
        DN += D

CD = CN

#print(CD)

C_count = B//C - (A-1)//C 
D_count = B//D - (A-1)//D
CD_count = B//CD - (A-1)//CD 



#print(C_count, D_count, CD_count)

print(B - A + 1 - C_count - D_count + CD_count)


### FIXED CODE ###


A, B, C, D = map(int, input().split())

def gcd(a, b):
    while b:
        a, b = b, a % b
    return a

def lcm(a, b):
    return a * b // gcd (a, b)


CD = lcm(C, D)

#print(CD)

C_count = B//C - (A-1)//C 
D_count = B//D - (A-1)//D
CD_count = B//CD - (A-1)//CD 



#print(C_count, D_count, CD_count)

print(B - A + 1 - C_count - D_count + CD_count)
### BUGGY CODE ###

# coding: utf-8
# Your code here!
n=int(input())
a=[]
b=[]
c=[]
for i in range(n):
    x=int(input())
    c.append(x)
    
dp=[0]
for i in range(n):
    tmp=dp
    for v in tmp:
        dp.append(v+c[i])
#dp.sort()[::-1]
ans=0
for i in dp:
    if dp[i]%10!=0:
        ans=max(dp[i],ans) 
print(ans)



### FIXED CODE ###

n=int(input())
a=[]
b=[]
for i in range(n):
  x=int(input())
  if x%10==0:
    b.append(x)
  else:
    a.append(x)
a.sort()
ans=sum(a)+sum(b)
if ans%10==0:
  if len(a)>0:
    ans-=a[0]
  else:
    ans=0
print(ans)
### BUGGY CODE ###

h, w, m = map(int, input().split())

h_bomb = [0 for _ in range(h)]
w_bomb = [0 for _ in range(w)]

bomb_xy = {}
for ij in range(m):
    y, x = map(int, input().split())
    h_bomb[y-1] += 1
    w_bomb[x-1] += 1
    bomb_xy[str(y-1)+str(x-1)] = 1

h_max = max(h_bomb)
h_max_index = [i for i, y in enumerate(h_bomb) if y == h_max]

ans = 0
# print("ans:", ans)
for j in h_max_index:
    for i in range(w):
        if str(j)+str(i) in bomb_xy:
            temp_max = h_bomb[j] + w_bomb[i] - 1
        else:
            temp_max = h_bomb[j] + w_bomb[i]

        # print("temp:", temp_max)
        if temp_max > ans:
            ans = temp_max

print(ans)


### FIXED CODE ###

import sys

h, w, m = map(int, input().split())

h_bomb = [0 for _ in range(h)]
w_bomb = [0 for _ in range(w)]

bomb_xy = {}
for ij in range(m):
    y, x = map(int, input().split())
    h_bomb[y-1] += 1
    w_bomb[x-1] += 1
    bomb_xy[str(y-1)+str(x-1)] = 1

h_max = max(h_bomb)
h_max_index = [i for i, y in enumerate(h_bomb) if y == h_max]
w_max = max(w_bomb)
w_max_index = [j for j, x in enumerate(w_bomb) if x == w_max]

ans = 0
# print("ans:", ans)
for j in h_max_index:
    for i in w_max_index:
        if str(j)+str(i) in bomb_xy:
            ans = h_bomb[j] + w_bomb[i] - 1
        else:
            print(h_bomb[j] + w_bomb[i])
            sys.exit()

print(ans)
### BUGGY CODE ###

n = int(input())

a = 1

while a <= n:
  b = a
  a **= 2
  
print(b)

### FIXED CODE ###

n = int(input())
 
a = 1
b = 0
c = 0

 
while c <= n:
  b = c
  c = a ** 2
  a += 1
  
print(b)
### BUGGY CODE ###

class UnionFind:
    def __init__(self,N):
        self.parent = [i for i in range(N)]
        self.rank = [0] * N
        self.count = 0
        self._size = [1]*N
    def root(self,a):
        if self.parent[a] == a:
            return a
        else:
            self.parent[a] = self.root(self.parent[a])
            return self.parent[a]
    def is_sama(self,a,b):
        return self.root(a) == self.root(b)
    def unite(self,a,b):
        ra = self.root(a)
        rb = self.root(b)
        if ra == rb:
            return
        if self.rank[ra] < self.rank[rb]:
            self.parent[ra] = rb
            self._size[rb] += self._size[ra]
        else:
            self.parent[rb] = ra
            if self.rank[ra] == self.rank[rb]:
                self.rank[ra] += 1
            self._size[ra] += self._size[rb]
        self.count += 1
    def print_info(self):
        print("parent", self.parent)
        print("rank", self.rank)
        print("count", self.count)
        print("size", self._size)
    def size(self,a):
        return self._size[self.root(a)]

import sys
input = sys.stdin.readline
ans = 0
N,M = map(int,input().split())
UF = UnionFind(N)
for i in range(M):
    A,B = map(int,input().split())
    A -= 1
    B -= 1
    UF.unite(A,B)

for i in range(N):
    for j in range(i+1,N):
        if not UF.is_sama(i,j):
            ans += 1
            UF.unite(i,j)
print(ans)

### FIXED CODE ###

import sys
from collections import deque
input = sys.stdin.readline

N,M = map(int,input().split())
table = [[] for i in range(N)]
Q = deque()
visited = [0]*N
ans = 0
for i in range(M):
    A,B = map(int,input().split())
    A -= 1
    B -= 1
    table[A].append(B)
    table[B].append(A)

for x in range(N):
    if visited[x] == 0:
        ans += 1
        Q.append(x)
        while Q:
            x = Q.popleft()
            for y in table[x]:
                if visited[y]==0:
                    Q.append(y)
                    visited[y] = 1

print(ans-1)
### BUGGY CODE ###

N=int(input())
check_lst=[]
ans=0
for i in range(N):
	check_lst.append([0]*26)
for i in range(N):
	s = input()
	for c in s:#a=97, z=122
		check_lst[i][ord(c)-97]+=1
for i in range(N-1):
	for j in range(i+1,N):
		if check_lst[i]==check_lst[j]:
			ans+=1
print(ans)

### FIXED CODE ###

N=int(input())
S = ["".join(sorted(input())) for _ in range(N)]
d={}
ans=0
for s in S:
	if s in d:
		ans+=d[s]
		d[s]+=1
	else:
		d[s]=1
print(ans)
### BUGGY CODE ###

n, m, k = map(int, input().split())
A = tuple(map(int, input().split()))
B = tuple(map(int, input().split()))
from itertools import accumulate
AS = [0] + list(accumulate(A))
BS = [0] + list(accumulate(B))

ans = 0
for i in range(n+1):
    if AS[i] > k:
        break
    for j in range(0, m+1):
        if AS[i] + BS[j] > k:
            break
        ans = max(ans, i+j)
        
print(ans)


### FIXED CODE ###

n, m, k = map(int, input().split())
A = tuple(map(int, input().split()))
B = tuple(map(int, input().split()))
from itertools import accumulate
AS = [0] + list(accumulate(A))
BS = [0] + list(accumulate(B))

ans = 0
j = m
for i in range(n+1):
    if AS[i] > k:
        break

    while AS[i] + BS[j] > k:
        j -= 1
    ans = max(ans, i+j)
        
print(ans)
### BUGGY CODE ###

import numpy as np
N, X, D = map(int, input().split())

if not D:
  if not X:
    print(1)
  else:
    print(N+1)

else:
  num_dict = dict()
  ans = 0
  for i in range(N+1):
    left_num = int(i*X/D) + int(i*(i-1)/2)
    right_num = int(i*X/D) + int(i*(2*N-1-i)/2)
    judge_num = i*X%D
    if not judge_num in num_dict:
      num_dict[judge_num] = [(left_num,right_num)]
    else:
      num_dict[judge_num].append((left_num,right_num))

  for j,k in num_dict.items():
    ans_set = set()
    for l in k:
      ans_set |= {i for i in range(l[0],l[1]+1)}
    ans += len(ans_set)
      
  print(ans)

### FIXED CODE ###

import numpy as np
N, X, D = map(int, input().split())

if not D:
  if not X:
    print(1)
  else:
    print(N+1)

else:
  num_dict = dict()
  ans = 0
  for i in range(N+1):
    left_num = int(i*X/D) + int(i*(i-1)/2)
    right_num = int(i*X/D) + int(i*(2*N-1-i)/2)
    judge_num = i*X%D
    if not judge_num in num_dict:
      num_dict[judge_num] = [(left_num,right_num)]
    else:
      num_dict[judge_num].append((left_num,right_num))

  for j,k in num_dict.items():
    new_k = sorted(k)
    L = new_k[0][0]
    R = new_k[0][1]
    for l in new_k:
      if l[0] <= R <= l[1]:
        R = l[1]
      elif R < l[0] and R < l[1]:
        ans += R-L+1
        L, R = l[0], l[1]
    ans += R-L+1
    
  print(ans)
### BUGGY CODE ###

from collections import Counter
from math import factorial
Q = 10**9+7
def primes(n):
    primfac = [0]
    d = 2
    while d*d <= n:
        while n%d == 0:
            primfac[-1] += 1
            n //= d
        d += 1
        if primfac[-1] != 0:
            primfac.append(0)
    if n > 1:
        if primfac[-1] == 0:
            primfac[-1] += 1
        else:
            primfac.append(1)
    return primfac
def combination(a,b):
    return ( (factorial(a)//factorial(b))//factorial(a-b))%Q
N, M = map( int, input().split())
C = primes(M)
ans = 1
if N == 1:
    print(1)
else:
    for x in C:
        ans = (ans * combination(x+N-1,N-1))%Q
    print(ans)


### FIXED CODE ###

from collections import Counter
from math import factorial
Q = 10**9+7
def primes(n):
    primfac = [0]
    d = 2
    while d*d <= n:
        while n%d == 0:
            primfac[-1] += 1
            n //= d
        d += 1
        if primfac[-1] != 0:
            primfac.append(0)
    if n > 1:
        if primfac[-1] == 0:
            primfac[-1] += 1
        else:
            primfac.append(1)
    return primfac
def combination(a,b):
    return ( (factorial(a)//factorial(b))//factorial(a-b))%Q
N, M = map( int, input().split())
C = primes(M)
ans = 1
if N == 1:
    print(1)
else:
    for x in C:
        ans = (ans * combination(x+N-1,N-1))%Q
    print(ans)