Problem Description

Given two positive integers $n, k(2 \le k \le n)$, Alice and Bob will play the following game:

• Alice needs to provide a sequence $a$ of length $k$ consisting of positive integers, such that $\sum\limits_{i = 1}^{k} a_i = n$.

• Bob needs to try to give a positive integer $m$ with $m \ge 2$, such that the positive integer sequence $a$ given by Alice can be partitioned into $m$ non-empty multisets, and the sums of elements in these multisets are all equal. If Bob can give such an integer $m$, then Bob wins; otherwise, Alice wins.

Assuming both players use optimal strategies, determine who will win. You need to answer $T$ queries.

Input Format

This problem contains multiple queries in a single test file.

The first line contains a positive integer $T$, representing the number of queries.

For each query: one line contains two positive integers $n, k$, with the meaning described in the Description.

Output Format

For each query, output one line Alice or Bob, indicating who will win.

2
4 4
8 3

Bob
Alice

Hint

Sample Explanation

For the first group of testdata, Alice can only provide the positive integer sequence $\left\{1,1,1,1\right\}$. Then Bob gives $m = 4$ and partitions the sequence into $\left\{\left\{1\right\},\left\{1\right\},\left\{1\right\},\left\{1\right\}\right\}$. Bob can also give $m = 2$ and partition the sequence into $\left\{\left\{1, 1\right\}, \left\{1, 1\right\}\right\}$, obtaining two multisets whose element sums are both $2$, which also satisfies the requirement.

For the second group of testdata, Alice can provide the positive integer sequence $\left\{3, 2, 3\right\}$. It can be proven that Bob has no valid partition plan at this time, so Alice wins.

Constraints

This problem uses bundled tests.

For $100\%$ of the data:

• $1 \le T \le 2 \times 10^5$;
• $2 \le k \le n \le 10^8$.

The detailed subtask allocation is as follows:

Translated by ChatGPT 5