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# Queries About Numbers CodeChef Solution

## Queries About Numbers CodeChef Solution in C++14

``````#include <bits/stdc++.h>
//for policy based ds //p.order_of_key() -> returns index of value //*p.find_by_order(3) ->value at index
#include <ext/pb_ds/assoc_container.hpp> // Common file
#include <ext/pb_ds/tree_policy.hpp>
#include <functional> // for less

using namespace __gnu_pbds; //for policy based ds
using namespace std;

#define int long long
#define pii pair<int, int>
#define vi vector<int>
#define maxHeap priority_queue<int>;
#define minHeap priority_queue<int, vi, greater<int>>
#define mod 1000000007
#define inf 1e18
#define rep(i, s, n) for (int i = s; i < n; i++)
#define sp(ans, pre) fixed << setprecision(pre) << y
#define pb push_back
#define srt(v) sort(v.begin(), v.end())
#define all(v) begin(v), end(v)
#define inputArr(i, arr) \
for (int &i : arr)   \
cin >> i;
#define ll long long
#define ull unsigned long long
#define lld long double
#define kickPrint(tt) cout << "Case #" << tt << ": "

typedef tree<pii, null_type, less<pii>, rb_tree_tag, tree_order_statistics_node_update> pbds;

time_t Begin;

//////////////////Debug///////////////
#define debug(x)       \
cout << #x << " "; \
_print(x);         \
cout << endl;
void _print(ll t)
{
cout << t;
}
//void _print(int t) {cout << t;}
void _print(string t) { cout << t; }
void _print(char t) { cout << t; }
void _print(lld t) { cout << t; }
void _print(double t) { cout << t; }
void _print(ull t) { cout << t; }
void display(ll a[], ll n)
{
for (ll i = 0; i < n; i++)
{
cout << a[i] << " ";
}
cout << endl;
}

template <class T, class V>
void _print(pair<T, V> p);
template <class T>
void _print(vector<T> v);
template <class T>
void _print(set<T> v);
template <class T, class V>
void _print(map<T, V> v);
template <class T>
void _print(multiset<T> v);
template <class T, class V>
void _print(pair<T, V> p)
{
cout << "{";
_print(p.first);
cout << ",";
_print(p.second);
cout << "}";
}
template <class T>
void _print(vector<T> v)
{
cout << "[ ";
for (T i : v)
{
_print(i);
cout << " ";
}
cout << "]";
}
template <class T>
void _print(set<T> v)
{
cout << "[ ";
for (T i : v)
{
_print(i);
cout << " ";
}
cout << "]";
}
template <class T>
void _print(multiset<T> v)
{
cout << "[ ";
for (T i : v)
{
_print(i);
cout << " ";
}
cout << "]";
}
template <class T, class V>
void _print(map<T, V> v)
{
cout << "[ ";
for (auto i : v)
{
_print(i);
cout << " ";
}
cout << "]";
}
template <typename T, typename U>
inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U>
inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }

void init()
{
Begin = clock();
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
#ifndef ONLINE_JUDGE
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif
}
void timeTaken()
{
#ifndef ONLINE_JUDGE
double time_taken = double(clock() - Begin) / double(CLOCKS_PER_SEC);
cout << "Execution Time: " << fixed << setprecision(5) << time_taken << "s\n";
#endif
}

vector<int> computeLps(string s, int M)
{
int len = 0;
vector<int> lps(M + 20);

lps[0] = 0;

int i = 1;
while (i < M)
{
if (s[i] == s[len])
{
len++;
lps[i] = len;
i++;
}
else
{
if (len != 0)
{
len = lps[len - 1];
}
else
{
lps[i] = 0;
i++;
}
}
}
// debug(len);
return lps;
}

int ceiling(int x, int y)
{
int res = x / y;
if (x % y)
{
if (x >= 0)
res++;
}
return res;
}

vector<vector<int>> makePrefix(vector<vector<int>> &grid)
{
int n = grid.size(), m = grid[0].size();
vector<vector<int>> prefix(n + 1, vector<int>(m + 1));

for (int i = 0; i < n; i++)
{
for (int j = 0; j < m; j++)
{
prefix[i + 1][j + 1] = grid[i][j] + prefix[i][j + 1] + prefix[i + 1][j] - prefix[i][j];
}
}

return prefix;
}

int query(int x1, int y1, int x2, int y2, vector<vector<int>> &prefix)
{
// cout << x1 << " " << y1 << " " << x2 << " " << y2 << endl;

// cout << "query: " << prefix[x2 + 1][y2 + 1] << " " << prefix[x2 + 1][y1] << " " << prefix[x1][y2 + 1] << " " << prefix[x1][y2] << endl;
return prefix[x2 + 1][y2 + 1] - prefix[x2 + 1][y1] - prefix[x1][y2 + 1] + prefix[x1][y1];
}

int toInt(string &s)
{
int res = 0;
for (char c : s)
res = res * 10 + (c - '0');
return res;
}

bool isValid(int i, int j, int n, int m)
{
return i >= 0 && i < n && j >= 0 && j < m;
}

int dx[] = {-1, 0, 0, 1};
int dy[] = {0, 1, -1, 0};

map<int, int> primeFactorization(int n)
{
map<int, int> mp;
for (int i = 2; i * i <= n; i++)
{
int exp = 0;
while (n % i == 0)
{
n /= i;
exp++;
}

if (exp)
mp[i] = exp;
}

if (n > 1)
{
mp[n] = 1;
}

return mp;
}

// const int MX = 100000;
int32_t main()
{
init();
//--------------------

int t = 1;
// cin >> t;
for (int tt = 1; tt <= t; tt++)
{
int n, q;
cin >> n >> q;

map<int, int> mp = primeFactorization(n);

int totalDivN = 1;
for (auto i : mp)
totalDivN *= i.second + 1;
// debug(mp);

while (q--)
{
int ty, k;
cin >> ty >> k;
int res = 1;
if (ty == 1)
{
int kk = k;
for (auto i : mp)
{
int cnt = 0;
while (kk % i.first == 0)
{
kk /= i.first;
cnt++;
}
res *= min(cnt, i.second) + 1;
}

if (n == 1)
res = 1;
}
else if (ty == 2)
{
int kk = k;
for (auto i : mp)
{
int cnt = 0;
while (kk % i.first == 0)
{
kk /= i.first;
cnt++;
}
res *= i.second - cnt + 1;
}

if (n % k != 0)
res = 0;
else if (n == k)
res = 1;
}
else
{
int kk = k;
for (auto i : mp)
{
int cnt = 0;
while (kk % i.first == 0)
{
kk /= i.first;
cnt++;
}
res *= i.second - cnt + 1;
}

if (n % k != 0)
res = 0;
else if (n == k)
res = 1;
res = totalDivN - res;
}
cout << res << "\n";
}
}

//---------------------------
timeTaken();
return 0;
}``````

## Queries About Numbers CodeChef Solution in PYTH 3

``````import sys

n,q=map(int,input().split())
pfactors=[]
num=n
i=2
while((i*i)<=num):
if num%i==0:
num//=i
pfactors.append(i)
else:
i+=1
if num!=1:
pfactors.append(num)
nd=dict()
kd=dict()
#print(pfactors)
for i in pfactors:
nd[i]=0
kd[i]=0
for i in pfactors:
nd[i]+=1
#print(nd)
#print(kd)

for _ in range(q):
t,k=map(int,input().split())
if t==1:
if n==1:
print(1)
else:
if k==1:
print(1)
else:
for i in pfactors:
if k%i==0:
kd[i]+=1
k//=i
ans=1
for i in kd:
ans*=(kd[i]+1)
print(ans)
for i in kd:
kd[i]=0
elif t==2:
if n==1:
if k==1:
print(1)
else:
print(0)
elif k==1:
ans=1
for i in nd:
ans*=(nd[i]+1)
print(ans)
else:
if n%k!=0:
print(0)
else:
for i in nd:
kd[i]=nd[i]
for i in pfactors:
if k%i==0:
kd[i]-=1
k//=i
ans=1
for i in kd:
ans*=(kd[i]+1)
print(ans)
for i in kd:
kd[i]=0
else:
if n==1:
if k==1:
print(0)
else:
print(1)
elif k==1:
print(0)
else:
if n%k!=0:
ans=1
for i in nd:
ans*=(nd[i]+1)
print(ans)
else:
ans1=1
for i in nd:
ans1*=(nd[i]+1)
for i in nd:
kd[i]=nd[i]
for i in pfactors:
if k%i==0:
kd[i]-=1
k//=i
ans2=1
for i in kd:
ans2*=(kd[i]+1)
print(ans1-ans2)
for i in kd:
kd[i]=0``````

## Queries About Numbers CodeChef Solution in C

``````#include <stdio.h>
#define Int long long int
Int a[30][2]={0};
Int total=1;
int  primefac(Int t){
int m=0;
for(Int i=2;i*i<=t;i++)
if(!(t%i)){
a[m++][0]=i;
while(!(t%i))a[m-1][1]++,t/=i;
}
if(t>1)
a[m++][0]=t,a[m-1][1]++;
for(int i=0;i<m;i++)
total*=(a[i][1]+1);

return m;

}
int min(int a,int b){
return a>b?b:a;
}
int main(){
Int n;
int q,t;
Int k;
scanf("%lld",&n);
int m=primefac(n);
scanf("%d",&q);
while(q--){
scanf("%d%lld",&t,&k);
Int res=1;
if(t==1){
for(int i=0;i<m;i++){

int u=0;
if(!(k%a[i][0])){
while(!(k%a[i][0])){
u++;
k/=a[i][0];
}}
res=res*1ll*(min(u,a[i][1])+1);
}
printf("%lld\n",res);}
else if(t==2){

if(n%k)
res=0;
else if(!(n%k)){
for(int i=0;i<m;i++){
int u=0;
if(!(k%a[i][0]) ){
while(!(k%a[i][0])){
u++;
k/=a[i][0];
}}
res=res*1ll*(a[i][1]-u+1);
}}
printf("%lld\n",res); }
else if(t==3){
if(n%k)
res=0;
else if(!(n%k)){
for(int i=0;i<m;i++){
int u=0;
if(!(k%a[i][0])){
while(!(k%a[i][0])){
u++;
k/=a[i][0];
}}
res=res*1ll*(a[i][1]-u+1);
}}
printf("%lld\n",total-res);

}

}
return 0;}``````

## Queries About Numbers CodeChef Solution in JAVA

``````
import java.io.IOException;
import java.util.*;

public class Main
{
static long total=1;
public static void main(String args[]) throws java.lang.Exception
{
FastScanner input = new FastScanner();
int t=1;
while(t-->0){

long N=input.nextLong();
long Q=input.nextLong();
HashMap<Long,Long> map=Factorize(N);
StringBuilder sb=new StringBuilder();
while(Q-->0){

int T=input.nextInt();
long K=input.nextLong();
if(T==1){
long ans=ResponseToQuery1(map,K);
sb.append(ans+"\n");
}else if(T==2){
long ans=ResponseToQuery2(map,K);
sb.append(ans+"\n");
}else if(T==3){
long ans=ResponseToQuery3(map,K);
sb.append(ans+"\n");
}
}
System.out.println(sb);
}

}
public static long ResponseToQuery3(HashMap<Long,Long>map,long K){
long val=ResponseToQuery2(map,K);
return (total-val);
}
public static long ResponseToQuery2(HashMap<Long,Long>map,long K){
long ans=1;
for(long key:map.keySet()){
long fac=key;
long val=map.get(key);
long cnt=0;
while(K%fac==0){
K/=fac;
cnt++;
}
if(cnt>val){
ans=0;break;
}

ans*=(val-cnt+1);
}
if(K>1)ans=0;
return ans;
}
public static long ResponseToQuery1(HashMap<Long,Long>map,long K){
// HashMap<Long,Long> qmap=new HashMap<>();
long ans=1;
for(long key:map.keySet()){
long fac=key;
long val=map.get(key);
long cnt=0;
while(K%fac==0){
K/=fac;
cnt++;
}
ans*=(Math.min(val,cnt)+1);

}

return ans;
}
public static HashMap<Long,Long> Factorize(long N){
HashMap<Long,Long> map=new HashMap<>();
for(long i=2;i*i<=N;i++){
if(N%i==0){
long f1=i;
long cnt=0;
while(N%f1==0){
N/=f1;cnt++;
}
if(cnt!=0)
map.put(f1,cnt);
total*=(cnt+1);
}
}
if(N>1){map.put(N,1L);total*=2;}
return map;
}

static class FastScanner
{

StringTokenizer st = new StringTokenizer("");

String next()
{
while (!st.hasMoreTokens()) {
try {
} catch (IOException e) {
e.printStackTrace();
}
}
return st.nextToken();
}

int nextInt()
{
return Integer.parseInt(next());
}

long nextLong()
{

return Long.parseLong(next());
}

double nextDouble()
{
return Double.parseDouble(next());
}

String nextLine() throws IOException
{
}
}

}``````

## Queries About Numbers CodeChef Solution in PYPY 3

``````from math import ceil,gcd,factorial,sqrt,log,log2
import queue
# import re
# from functools import reduce
#product is used to generater truth tables or multiply list produc([0,1],repeat=n)
from itertools import permutations,combinations,accumulate,product
from collections import Counter,deque
from sys import stdin,stdout
from bisect import bisect,insort,bisect_left,insort_left
# bisect=upper_bound,bisect_left=lower_bound
def sieve(n):
prime = [True]*(n+1)
p = 2
a=[]
for p in range(2,int(n**0.5)+1):
if (prime[p] == True):
a.append(p)
for l1 in range(p * p, n+1, p):
prime[l1] = False
return a
def simplesieve(n):
prime=[2]
mark=[False]*(n+1)
for p in range(3,n+1,2):
if(mark[p]==False):
prime.append(p)
if(p*p<=n):
for l1 in range(p*p,n +1,2*p):
mark[l1]=True
return prime
def segementedsieve(low,high):
primes=simplesieve(int(high**.5))
prime = [True] * (high-low + 1)
for i in primes:
lower = (low//i)*i
if lower<low:
lower+=i
for j in range(lower,high+1,i):
if(j!=i):
prime[j-low]=False
ans=[]
for i in range(low,high+1):
if prime[i-low]:
ans.append(i)
return ans
def isprime(n):
if(n==2):
return True
if(n%2==0 or n==1):
return False
for l1 in range(3,int(n**0.5)+1,2):
if(n%l1==0):
return False
return True
def binpow(a,b,m):
r2=1
a=a%m
while(b>0):
if(b&1):
r2=(r2*a)%m
a=(a*a)%m
b>>=1
return r2
def lcm(a,b):
return (a//gcd(a,b))*b
#gcd(a,b)=ax+by and

def gcdExtended(a,b):
if(b==0):
return a,1,0
g,x1,y1=gcdExtended(b,a%b)
x1,y1 = y1,x1-(a//b)*y1
return g,x1,y1
def binsearch(a,l,r,key):
while(r-l>1):
m=l+(r-l)//2
if(a[m]<=key):
l=m
else:
r=m
if(a[l]==key):
return l
if(a[r]==key):
return r
return -1
class Node():
def __init__(self, data):
self.data = data
self.left = None
self.right = None
def inorder(root):
res, stack = [], []
current = root
while True:
while current:
stack.append(current)
current = current.left
if len(stack) == 0:
return res
node = stack[-1]
stack.pop(len(stack)-1)
if node.data != None:
res.append(node.data)
current = node.right
return res

def dfs(graph,s,v,ans):
v[s]=1
ans.append(s)
for i in graph[s]:
if(v[i]==0):
dfs(graph,i,v,ans)
def bfs(graph,n,x,dest):
v=[0]*(1+n)
d=[0]*(1+n)
# d=[-1]*1000
d[x]=0
v[x]=1
q=queue.Queue()
q.put(x)
# p=[0]*(1+n)
# p[x]=-1
while(not q.empty()):
z=q.get()
for s in graph[z]:
if(v[s]==0):
v[s]=1
d[s]=d[z]+1
q.put(s)
# p[s]=z
# path=[]
# #l1=dest#given
# while(l1!=-1):
#    path.append(l1)
#    l1=p[l1]
# path.reverse()
#?print(d)
return d[dest]
# for _ in range(int(input())):
# n=int(input())
n,q=map(int,input().split())
# a=list(map(int,input().split()))
prime=Counter()
r=1
for i in range(2,int(n**0.5)+1):
if(n%i==0):
c=0
while(n%i==0):
n=n//i
c+=1
prime[i]=c
r=r*(c+1)
if(n>1):
prime[n]=1
r=r*2
t=len(prime)
for _ in range(q):
a,b=map(int,input().split())
c=Counter()
ans=1
if(a==1):
for i in prime:
if(b%i==0):
c=0
while(b%i==0):
b=b//i
c+=1
ans*=min(prime[i]+1,(c+1))
elif(a==2):
for i in prime:
if(b%i==0):
c=0
while(b%i==0):
b=b//i
c+=1
if(c>prime[i]):
ans=0
break
ans*=((prime[i]-c)+1)
else:
ans*=(prime[i]+1)
if(b>1):
ans=0
else:
for i in prime:
if(b%i==0):
c=0
while(b%i==0):
b=b//i
c+=1
if(c>prime[i]):
ans=0
break
ans*=((prime[i]-c)+1)
else:
ans*=(prime[i]+1)
if(b>1):
ans=0
ans=r-ans
print(ans)``````
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