There is a sequence $A_0, A_1, \ldots, A_{n-1}$ of length $n$. Write a program to execute the following queries:

• 1 l r c: Add $c$ to all $A_i$ in the interval $l \le i \le r$.
• 2 l r d: Replace all $A_i$ in the interval $l \le i \le r$ with $\lfloor A_i/d \rfloor$.
• 3 l r: Output the minimum of all $A_i$ in the interval $l \le i \le r$.
• 4 l r: Output the sum of all $A_i$ in the interval $l \le i \le r$.

where $\lfloor x \rfloor$ denotes the greatest integer $y$ such that $y \le x$ (for example, $\lfloor -2.5 \rfloor = -3$, $\lfloor -7 \rfloor = -7$).

Input

The first line contains two integers $n$ and $q$ ($1 \le n, q \le 100{,}000$), indicating the length of the sequence and the number of queries.

The second line contains $n$ integers $A_0, A_1, \ldots, A_{n-1}$ ($-10^9 \le A_i \le 10^9$).

Each of the next $q$ lines contains a query ($0 \le l \le r \le n-1$, $-10^4 \le c \le 10^4$, $2 \le d \le 10^9$).

Output

Whenever a query of type 3 or type 4 is encountered, output one answer per line.

Examples

Input 1

10 10
-5 -4 -3 -2 -1 0 1 2 3 4
1 0 4 1
1 5 9 1
2 0 9 3
3 0 9
4 0 9
3 0 1
4 2 3
3 4 5
4 6 7
3 8 9

Output 1

-2
-2
-2
-2
0
1
1