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Codeforces Round 356 (Div. 1) |
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data structures

*3100

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E. Bear and Bad Powers of 42

time limit per test

5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLimak, 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 i — print
*t*_{i}in a separate line. - 2 a b x — for set
*t*_{i}to*x*. It's guaranteed that*x*is a good number. - 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.

Input

The first line of the input contains two integers *n* and *q* (1 ≤ *n*, *q* ≤ 100 000) — 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.

Output

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

Example

Input

6 12

40 1700 7 1672 4 1722

3 2 4 42

1 2

1 3

3 2 6 50

1 2

1 4

1 6

2 3 4 41

3 1 5 1

1 1

1 3

1 5

Output

1742

49

1842

1814

1822

43

44

107

Note

After a query 3 2 4 42 the sequence is 40, 1742, 49, 1714, 4, 1722.

After a query 3 2 6 50 the sequence is 40, 1842, 149, 1814, 104, 1822.

After a query 2 3 4 41 the sequence is 40, 1842, 41, 41, 104, 1822.

After a query 3 1 5 1 the sequence is 43, 1845, 44, 44, 107, 1822.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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