Fix an Off-by-One Array Loop

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

An array has logical size $n$, so its valid indices are $0,1,\ldots,n-1$. A program intends to traverse it using for (i = 0; i <= b; ++i) and accesses $a_i$ at every iteration.

Determine whether this loop is safe. If $b\ge n$, the first out-of-bounds access occurs at index $n$. Do not attempt to predict the value of $a_n$ because that access is outside the valid array range.

Input

One line contains two integers $n$ and $b$, where $n\ge1$ and $b\ge0$.

Output

• If every index from $0$ through $b$ is valid, print SAFE.
• Otherwise print OUT_OF_BOUNDS x, where $x$ is the first invalid index.

Subtasks

Subtask 1 (20 points): $1\le n\le100$, $b=n-1$.

Subtask 2 (30 points): $1\le n\le1000$, $b=n$.

Subtask 3 (50 points): $1\le n\le10^9$, $0\le b\le2n$.

Examples

Input

5 5

Output

OUT_OF_BOUNDS 5

Explanation

For $n=5$, only indices $0,1,2,3,4$ are valid. Since the loop condition is $i\le5$, after processing $i=4$ it still executes once with $i=5$. Index $5=n$ is outside the array, so the first invalid index is $5$.