Make It One CodeChef Solution

We Are Discuss About CODECHEF SOLUTION

Make It One CodeChef Solution

Make It One CodeChef Solution

Answers will be Uploaded Shortly and it will be Notified on Telegram, So JOIN NOW
JoinScishowEngineerTelegram

Problem

Chef is given a positive integer N and we have to convert it to 1 using some operations.\newline

In one operation, Chef can do the following:\newline

  • Choose a prime number p such that p | N (p divides N).
  • Replace N with \frac{N}{p}.

However, Chef is also given some triggers of the form (a,b) (a is prime). Thus, if we divide by p in some operation, we also have to multiply by x for all triggers of the form (p,x).

For example: Consider N=18, and the triggers (3,4) and (3,2) exist. In one operation, if we choose to divide by 3, we have to multiply the result with 4 and 2. In other words, (18 \mapsto \frac{18}{3} \cdot 4 \cdot 2)=48. Thus, 18 is converted to 48.

Given a number N and M triggers of the form (a,b) (where a is always prime), find the minimum number of operations required to convert N to 1 modulo 998244353. Print -1 if it is not possible to do so.

Input Format

  • The first line of each input contains two integers N and M – the initial integer and the number of triggers given to the Chef.
  • The next M lines describe the triggers. The i^{th} of these M lines contains two space-separated integers a and b, denoting that Chef has to multiply by b if he choses to divide by a in some operation.
  • It is guaranteed that (a_i, b_i) \ne (a_j, b_j) for i \ne j.

Output Format

Output on a new line, the minimum number of operations required to convert N to 1, or print -1 if it is not possible to do so. In case it is possible to convert N to 1, the minimum number of operations can be large, so output it modulo 998244353.

Constraints

  • 1 \leq N \leq 10^6
  • 0 \leq M \leq 10^5
  • 1 \leq a \leq 10^6
  • 1 \leq b \leq 10^6
  • a is a prime number.

Sample 1:

Input

Output

6 1
2 3
3

Explanation:

We can convert 6 to 1 using 3 operations in the following way:

  • Divide 6 by 3. Since no trigger of the form (3,x) exists, 6 converts to \frac{6}{3}= 2.
  • Divide 2 by 2. Since (2,3) exists, 2 is converted to 2 \mapsto \frac{2}{2} \cdot 3 = 3. – Divide 3 by 3. Since no trigger of the form (3,x) exists, 3 converts to \frac{3}{3}= 1.

It can be proven that we cannot convert 6 to 1 in less than 3 operations.

Sample 2:

Input

Output

4 3
2 5
2 3
3 7
8

Sample 3:

Input

Output

2 3
2 3
3 5
5 3
-1

Explanation:

We can not convert 2 to 1 using any finite number of operations.

Answers will be Uploaded Shortly and it will be Notified on Telegram, So JOIN NOW
JoinScishowEngineerTelegram

 

SOLUTION

Make It One CodeChef Solution

Yhaa You have done it but next? if YOU Want to Get Others Please Visit Here JOIN NOW

Answers will be Uploaded Shortly and it will be Notified on Telegram, So JOIN NOW
JoinScishowEngineerTelegram

Related Posts

Leave a Reply

Your email address will not be published.

adplus-dvertising