Where is the Marble?

Source: UVa

Version: Phuoc Hung OJ Extended

Problem Statement

There are $n$ marbles. Each marble has a non-negative integer written on it. The marbles are initially unsorted.

Sort the marbles in increasing order. After sorting, positions are numbered from $1$ to $n$.

For each of $q$ query values $x$:

• if $x$ occurs, find its first position in the sorted sequence;
• otherwise report that it was not found.

Input

The first line contains $n$ and $q$.

The second line contains the $n$ marble values.

The third line contains $q$ query values.

Output

First print:

CASE# 1:

For each query $x$, print either:

x found at y

where $y$ is the first 1-based position of $x$, or:

x not found

Subtasks

• Subtask 1 — 20%: $1\le n,q\le100$.
• Subtask 2 — 30%: $1\le n,q\le2000$.
• Subtask 3 — 50%: $1\le n,q\le10000$, every input value is in $[0,10000]$.

Examples

Input

5 2
1 3 3 3 1
2 3

Output

CASE# 1:
2 not found
3 found at 3

Explanation

After sorting, the sequence is $[1,1,3,3,3]$. The value $2$ is absent, while the first $3$ is at 1-based position $3$.