UVA_10780.cpp

#include <bits/stdc++.h>
using namespace std;
#define F first
#define S second
#define PB push_back
#define PF push_front
#define P push
#define INC(i,a,b) for (ll i = a; i <= b; i++)
#define DEC(i,b,a) for (ll i = b; i >= a ; i--)
#define inf LLONG_MAX
#define neginf LLONG_MIN
#define mod  1000000007
#define eps 1e-9
typedef ostringstream OS ;
typedef stringstream SS ;
typedef long long ll ;
typedef unsigned long long ull;
typedef pair < ll , ll > PLL ;
typedef pair < char,ll > PCL ;
typedef deque < double > DD ;
typedef deque < PCL > DCL ;
typedef deque < ll > DL ;
typedef deque < PLL > DLL ;
typedef deque < char > DC ;
typedef deque < string > DS ;
typedef vector < double > VD;
typedef vector < PCL > VCL ;
typedef vector < ll > VL;
typedef vector < PLL > VLL ;
typedef vector < char > VC ;
typedef vector < string > VS ;
typedef map < ll ,ll > MLL ;
typedef map < char,ll > MCL;
typedef map < ll,char > MLC;
typedef map < string,ll> MSL;
typedef priority_queue < PLL > PQLL ;
typedef priority_queue < ll > PQL ;
typedef stack < ll > SKL ;
typedef stack < PLL > SKLL ;
typedef queue < ll > QL ;
typedef queue < PLL > QLL ;
typedef set < ll > SL ;
typedef set < PLL > SLL ;
typedef set < char > SC ;
 
string numtostr(ll n) {
     OS str1 ;
     str1 << n ;
     return str1.str();
}
ll strtonum(string s) {
     ll x ;
     SS str1(s);
     str1 >> x ;
     return x ;
}
ll GCD(ll a, ll b) {
    if ( b == 0 ) return a ;
    else return GCD(b,a%b);
}
ll LCM(ll a , ll b) {
    ll gcd = GCD(a,b);
     return (a/gcd)*b ;
}
ll  check[10005];
VL primes ;
void sieve(ll n) {
    memset(check,0,sizeof(check));
    check[1] = 1 ;
    for ( ll i = 4 ; i <= n ; i = i+2) check[i] = 1 ;    //the numbers which are not prime that means even numbers are marked by 1

    for ( ll i = 3 ; i*i <= n ; i += 2) {                // Even numbers are not prime so we will check only odd numbers and increment the number by 2 to avoid even number.
        if (!check[i]) {                                 // if  check[i] = 0 that means if the i value is a prime we will procced
            for ( ll j = i*i ; j <= n ; j += 2*i){       // here we are starting not by j = i+i we are starting by j = i*i because the numbers less than i*i are already 
                   check[j] = 1 ;                        // checked by the numbers less than j so no need to calculate them further . and each time we will increment the
            }                                            // numbers by 2*i because if this is a odd number then just incrementing i it will be even and even numbers 
        }                                                // numbers are not prime so no need to check this .
    }   

    for ( ll i = 1 ; i <= n ; i++)  if (!check[i]) primes.PB(i);   // only taking the primes numbers in vector
    return ;
}
MLL primefactorize(ll n) {
    MLL primefactors ;
    if ( n == 1)  return primefactors;
    for ( ll i = 0 ; primes[i] <= sqrt(n) && i < primes.size() ; i++) {
        while (!(n%primes[i])) {
            n = n/primes[i];
            primefactors[primes[i]]++ ;
        }
    }
    if ( n > 1 ) primefactors[n]++ ;
    return primefactors ;
}
MLL factorialfactorization(ll n) {
    MLL factors ;
    if ( n == 1) return factors ;
    for ( ll i = 0 ; primes[i] <= n && i < primes.size() ; i++) {
        ll freq = 0 ;
        ll x = n ;
        while(x) {
            freq += x/primes[i];
            x = x/primes[i];
        }
        if ( freq != 0) factors[primes[i]] = freq ; 
    }
    return factors ;
}
 
int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    sieve(10000);
    ll t,c = 0 ;
    scanf("%lld",&t);
    while(t--) {
        ll m,n ;
        scanf("%lld %lld",&m,&n);
        MLL factorsM,factorsN ;
        factorsM = primefactorize(m);
        factorsN = factorialfactorization(n);
        printf("Case %lld:\n",++c);
        if ( factorsN.size() == 0) printf("0\n");
        else {
            ll f = 0 ;
            ll minimum = inf ;
            for ( auto it = factorsM.begin() ; it != factorsM.end() ; it++) {
                if ( factorsN[it->first] < it->second) {
                    f = 1 ;
                    break ;
                }
                else minimum = min(minimum,factorsN[it->first]/it->second); 
            }
            if ( f) printf("Impossible to divide\n");
            else printf("%lld\n",minimum);
        } 
        
    }
 
    return 0 ;
}