A10405 | Bear and Bad Powers of 42

Limak, a bear, isn't good at handling queries. So, he asks you to do it.

We say that powers of $42$ (numbers $1,42,1764,...$ ) are bad. Other numbers are good.

You are given a sequence of $n$ good integers $t_{1},t_{2},...,t_{n}$ . Your task is to handle $q$ queries of three types:

1. 1 i — print $t_{i}$ in a separate line.
2. 2 a b x — for  set $t_{i}$ to $x$ . It's guaranteed that $x$ is a good number.
3. 3 a b x — for  increase $t_{i}$ by $x$ . After this repeat the process while at least one $t_{i}$ is bad.

You can note that after each query all $t_{i}$ are good.

The first line of the input contains two integers $n$ and $q$ ( $1<=n,q<=100000$ ) — the size of Limak's sequence and the number of queries, respectively.

The second line of the input contains $n$ integers $t_{1},t_{2},...,t_{n}$ ( $2<=t_{i}<=10^{9}$ ) — initial elements of Limak's sequence. All $t_{i}$ are good.

Then, $q$ lines follow. The $i$ -th of them describes the $i$ -th query. The first number in the line is an integer $type_{i}$ ( $1<=type_{i}<=3$ ) — the type of the query. There is at least one query of the first type, so the output won't be empty.

In queries of the second and the third type there is $1<=a<=b<=n$ .

In queries of the second type an integer $x$ ( $2<=x<=10^{9}$ ) is guaranteed to be good.

In queries of the third type an integer $x$ ( $1<=x<=10^{9}$ ) may be bad.

For each query of the first type, print the answer in a separate line.