Problem: You are given positive integers N and M.  How many sequences a of length N consisting of positive integers satisfy a_1 \times a_2 \times ... \times a_N = M? Find the count modulo 10^9+7.  Here, two sequences a' and a'' are considered different when there exists some i such that a_i' \neq a_i''.

Submission attempts (in order):
iN,iM = [int(x) for x in input().split()]
iD = 10**9 +7 

def fPrimeCounter(iM):
    iS = int(iM ** 0.5) + 1
    aRet = []
    for i in range(2,iS):
        iCounter = 0
        while iM % i == 0:
            iM = iM // i
            iCounter += 1
        if 0 < iCounter : aRet.append(iCounter)
    return aRet



def fBiPow(iX,iN,iD):
    iY = 1
    while iN > 0:
        if iN % 2 == 0:
            iX = iX * iX % iD
            iN = iN // 2
        else:
            iY = iX * iY % iD
            iN = iN - 1
    return iY

aP = fPrimeCounter(iM)
if aP == [] :
    print (1)
else:
    iMax = max(aP) + iN - 1
    aM = [1] * (iMax + 1)
    
    for i in range(1,iMax + 1):
        aM[i] = aM[i-1] * i  % iD
    aInvM = [1]* (iMax + 1)
    aInvM[iMax] = fBiPow(aM[iMax],iD-2,iD)
    
    for i in range(iMax,0,-1):
        aInvM[i-1] = aInvM[i]*i % iD

    iRet = 1
    for i in aP:
        
        iRet *= aM[i+iN-1] * aInvM[iN-1] * aInvM[i] % iD
    iRet %= iD
    print(iRet)


iN,iM = [int(x) for x in input().split()]
iD = 10**9 +7 

def fPrimeCounter(iM):
    i = 2
    iS = int(iM ** 0.5) + 1
    aRet = []
    while i < iS:
        iCounter = 0
        while iM % i == 0:
            iM = iM // i
            iCounter += 1
        if 0 < iCounter : aRet.append(iCounter)
        i += 1

    return aRet


def fBiPow(iX,iN,iD):
    iY = 1
    while iN > 0:
        if iN % 2 == 0:
            iX = iX * iX % iD
            iN = iN // 2
        else:
            iY = iX * iY % iD
            iN = iN - 1
    return iY

aP = fPrimeCounter(iM)
if aP == [] :
    print (1)
else:
    iMax = max(aP) + iN - 1
    aM = [1] * (iMax + 1)
    
    for i in range(1,iMax + 1):
        aM[i] = aM[i-1] * i  % iD
    aInvM = [1]* (iMax + 1)
    aInvM[iMax] = fBiPow(aM[iMax],iD-2,iD)
    
    for i in range(iMax,0,-1):
        aInvM[i-1] = aInvM[i]*i % iD

    iRet = 1
    for i in aP:
        
        iRet *= aM[i+iN-1] * aInvM[iN-1] * aInvM[i] % iD
    iRet %= iD
    print(iRet)


iN,iM = [int(x) for x in input().split()]
iD = 10**9 +7 

def fPrimeCounter(iM):
    i = 2
    iS = int(iM ** 0.5) + 1
    aRet = []
    while i < iS:
        iCounter = 0
        while iM % i == 0:
            iM = iM // i
            iCounter += 1
        if 0 < iCounter : aRet.append(iCounter)
        i += 1
        if iM == 1: break

    return aRet


def fBiPow(iX,iN,iD):
    iY = 1
    while iN > 0:
        if iN % 2 == 0:
            iX = iX * iX % iD
            iN = iN // 2
        else:
            iY = iX * iY % iD
            iN = iN - 1
    return iY

aP = fPrimeCounter(iM)
if aP == [] :
    print (1)
else:
    iMax = max(aP) + iN - 1
    aM = [1] * (iMax + 1)
    
    for i in range(1,iMax + 1):
        aM[i] = aM[i-1] * i  % iD
    aInvM = [1]* (iMax + 1)
    aInvM[iMax] = fBiPow(aM[iMax],iD-2,iD)
    
    for i in range(iMax,0,-1):
        aInvM[i-1] = aInvM[i]*i % iD

    iRet = 1
    for i in aP:
        
        iRet *= aM[i+iN-1] * aInvM[iN-1] * aInvM[i] % iD
    iRet %= iD
    print(iRet)



iN,iM = [int(x) for x in input().split()]
iD = 10**9 +7 

def fPrimeCounter(iM):
    iS = int(iM ** 0.5) + 1
    aRet = []
    for i in range(2,iS + 1):
        iCounter = 0
        while iM % i == 0:
            iM /= i
            iCounter += 1
        if 0 < iCounter : aRet.append(iCounter)
        if iM == 1 : break
    if 1 < iM  : aRet.append(1)
    return aRet
def fnCr(iN,iR,iD):
    iR = min(iR,iN-iR)
    if iR == 0 :
        return 1
    elif iR == 1 :
        return iN
    return (iN % iD) * pow(iR,iD-2,iD) * fnCr(iN-1,iR-1,iD) % iD

aP = fPrimeCounter(iM)
#if aP == []:
#   print(1)
#   exit()
iRet = 1
for i in aP:
    
    iRet *= fnCr(i+iN-1,i,iD)
iRet %= iD
print(iRet)


Verdicts: Wrong Answer

Wrong Answer

Wrong Answer

Accepted