statement_md.txt

Mirzapur Election

Jas and Ashish are the President and Vice-president of CSIT Party and are working hard to win the elections of Mirzapur.

There are **N** states in Mirzapur, whose vote counts on Day 0 are given. (*count[0,....,n-1]*) .

Next **D** days, either the vote count of a state gets updated, or the election commission wants Jas and Ashish to submit their Max-Potential Value.

**Max-Potential** =  maximum of gcd(count[i],count[j]), for all i, j.  ($ 0 \leq i, j \leq n-1, i \neq j $).

Mathematically, the two operations can be defined as:
* **[1 i x]**: Update voteCount of state i to x. (*count[i] = x*). 
* **[2]**: Output Max-Potential.


See the explanation of sample test cases, for more clarity.

Warning: **Use Fast IO**

###Input
* The first line contains space-separated integers **N, D**.
* The second line contains N space-separated integers **count[0],count[1] ...count[n-1]**.
* Next **D** line contains input corresponding to one of the operations mentioned below.
	* Operation 1:  **1 i x** (3 space-separarted integer)
	* Operation 2:  **2**

###Output
For every Operation 2, output the Max-Potential on a new line.

###Constraints
* $2 \leq N \leq 100000$
* $1 \leq D, x \leq 100000$
* $0 \leq i \leq n-1$
* $1 \leq count[i] \leq 100000$

###Example Input
```
5 5
1 1 3 4 5
2
1 1 2
2
1 4 3
2
```
###Example Output
```
1
2
3
```
###EXPLANATION:
* On Day 0, count = [1,1,3,4,5]
* On Day 1, Max-Potential = 1, gcd of all pairs of states is 1.
* On Day 2, count = [1,2,3,4,5]
* On Day 3, Max-Potential = 2, gcd of states 1,3 is gcd(2,4) = 2.
* On Day 4, count = [1,2,3,4,3]
* On Day 5, Max-Potential = 3, gcd of states 2,4 is gcd(3,3) = 3.