G. Periodic RMQ Problem
time limit per test
4 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

You are given an array a consisting of positive integers and q queries to this array. There are two types of queries:

• 1 l r x — for each index i such that l ≤ i ≤ r set ai = x.
• 2 l r — find the minimum among such ai that l ≤ i ≤ r.

We decided that this problem is too easy. So the array a is given in a compressed form: there is an array b consisting of n elements and a number k in the input, and before all queries a is equal to the concatenation of k arrays b (so the size of a is n·k).

Input

The first line contains two integers n and k (1 ≤ n ≤ 105, 1 ≤ k ≤ 104).

The second line contains n integers — elements of the array b (1 ≤ bi ≤ 109).

The third line contains one integer q (1 ≤ q ≤ 105).

Then q lines follow, each representing a query. Each query is given either as 1 l r x — set all elements in the segment from l till r (including borders) to x (1 ≤ l ≤ r ≤ n·k, 1 ≤ x ≤ 109) or as 2 l r — find the minimum among all elements in the segment from l till r (1 ≤ l ≤ r ≤ n·k).

Output

For each query of type 2 print the answer to this query — the minimum on the corresponding segment.

Examples
Input
3 11 2 332 1 31 1 2 42 1 3
Output
13
Input
3 21 2 352 4 41 4 4 52 4 41 1 6 12 6 6
Output
151