Problem:


Score : 400 points

Problem Statement

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''.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq M \leq 10^9

Input

Input is given from Standard Input in the following format:

N M

Output

Print the number of the sequences consisting of positive integers that satisfy the condition, modulo 10^9 + 7.

Sample Input 1

2 6

Sample Output 1

4

Four sequences satisfy the condition: \{a_1, a_2\} = \{1, 6\}, \{2, 3\}, \{3, 2\} and \{6, 1\}.

Sample Input 2

3 12

Sample Output 2

18

Sample Input 3

100000 1000000000

Sample Output 3

957870001



Sample input:
2 6


Sample output:
4

Submission status: Wrong Answer

Solution code:
import math
MOD=10**9 + 7
N,M=map(int,input().split())
plist = 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,33349,33353,33359,33377,33391,33403,33409,33413,33427,33457,33461,33469,33479,33487,33493,33503,33521,33529,33533,33547,33563,33569,33577,33581,33587,33589,33599,33601,33613,33617,33619,33623,33629,33637,33641,33647,33679,33703,33713,33721,33739,33749,33751,33757,33767,33769,33773,33791,33797,33809,33811,33827,33829,33851,33857,33863,33871,33889,33893,33911,33923,33931,33937,33941,33961,33967,33997,34019,34031,34033,34039,34057,34061,34123,34127,34129,34141,34147,34157,34159,34171,34183,34211,34213,34217,34231,34253,34259,34261,34267,34273,34283,34297,34301,34303,34313,34319,34327,34337,34351,34361,34367,34369,34381,34403,34421,34429,34439,34457,34469,34471,34483,34487,34499,34501,34511,34513,34519,34537,34543,34549,34583,34589,34591,34603,34607,34613,34631,34649,34651,34667,34673,34679,34687,34693,34703,34721,34729,34739,34747,34757,34759,34763,34781,34807,34819,34841,34843,34847,34849,34871,34877,34883,34897,34913,34919,34939,34949,34961,34963,34981,35023,35027,35051,35053,35059,35069,35081,35083,35089,35099,35107,35111,35117,35129,35141,35149,35153,35159,35171,35201,35221,35227,35251,35257,35267,35279,35281,35291,35311,35317,35323,35327,35339,35353,35363,35381,35393,35401,35407,35419,35423,35437,35447,35449,35461,35491,35507,35509,35521,35527,35531,35533,35537,35543,35569,35573,35591,35593,35597,35603,35617,35671,35677,35729,35731,35747,35753,35759,35771,35797,35801,35803,35809,35831,35837,35839,35851,35863,35869,35879,35897,35899,35911,35923,35933,35951,35963,35969,35977,35983,35993,35999,36007,36011,36013,36017,36037,36061,36067,36073,36083,36097,36107,36109,36131,36137,36151,36161,36187,36191,36209,36217,36229,36241,36251,36263,36269,36277,36293,36299,36307,36313,36319,36341,36343,36353,36373,36383,36389,36433,36451,36457,36467,36469,36473,36479,36493,36497,36523,36527,36529,36541,36551,36559,36563,36571,36583,36587,36599,36607,36629,36637,36643,36653,36671,36677,36683,36691,36697,36709,36713,36721,36739,36749,36761,36767,36779,36781,36787,36791,36793,36809,36821,36833,36847,36857,36871,36877,36887,36899,36901,36913,36919,36923,36929,36931,36943,36947,36973,36979,36997,37003,37013,37019,37021,37039,37049,37057,37061,37087,37097,37117,37123,37139,37159,37171,37181,37189,37199,37201,37217,37223,37243,37253,37273,37277,37307,37309,37313,37321,37337,37339,37357,37361,37363,37369,37379,37397,37409,37423,37441,37447,37463,37483,37489,37493,37501,37507,37511,37517,37529,37537,37547,37549,37561,37567,37571,37573,37579,37589,37591,37607,37619,37633,37643,37649,37657,37663,37691,37693,37699,37717,37747,37781,37783,37799,37811,37813,37831,37847,37853,37861,37871,37879,37889,37897,37907,37951,37957,37963,37967,37987,37991,37993,37997,38011,38039,38047,38053,38069,38083,38113,38119,38149,38153,38167,38177,38183,38189,38197,38201,38219,38231,38237,38239,38261,38273,38281,38287,38299,38303,38317,38321,38327,38329,38333,38351,38371,38377,38393,38431,38447,38449,38453,38459,38461,38501,38543,38557,38561,38567,38569,38593,38603,38609,38611,38629,38639,38651,38653,38669,38671,38677,38693,38699,38707,38711,38713,38723,38729,38737,38747,38749,38767,38783,38791,38803,38821,38833,38839,38851,38861,38867,38873,38891,38903,38917,38921,38923,38933,38953,38959,38971,38977,38993,39019,39023,39041,39043,39047,39079,39089,39097,39103,39107,39113,39119,39133,39139,39157,39161,39163,39181,39191,39199,39209,39217,39227,39229,39233,39239,39241,39251,39293,39301,39313,39317,39323,39341,39343,39359,39367,39371,39373,39383,39397,39409,39419,39439,39443,39451,39461,39499,39503,39509,39511,39521,39541,39551,39563,39569,39581,39607,39619,39623,39631,39659,39667,39671,39679,39703,39709,39719,39727,39733,39749,39761,39769,39779,39791,39799,39821,39827,39829,39839,39841,39847,39857,39863,39869,39877,39883,39887,39901,39929,39937,39953,39971,39979,39983,39989]
dic = {}
for p in plist:
    dic[p] = 0
for p in plist:
    while M%p == 0:
        M/=p
        dic[p]+=1
L = N + 40
fact = [1 for _ in range(L)]
invfact = [1 for _ in range(L)]
for i in range(1,L):
    fact[i]=(fact[i-1]*i)%MOD
    invfact[i]=(invfact[i-1]*pow(i,MOD-2,MOD))%MOD
ans = 1
for p in dic:
    if dic[p] !=0:
        ans *= fact[N-1+dic[p]]*invfact[N-1]*invfact[dic[p]] %MOD
print(ans%MOD)