CF2179A Blackslex and Password

Blackslex is designing a log-in system for Gean Dev and discovered that most users use weak passwords. To resolve this issue, he posed the following conditions, dependent on two variables $ k $ and $ x $ , for all passwords. Each password is a string $ s $ of length $ n $ satisfying these properties. - $ s $ uses only the first $ k $ lowercase letters of the English alphabet. - For every pair of indices $ 1 \le i < j \le n $ such that $ (j-i) $ is divisible by $ x $ , the letters $ s_i $ and $ s_j $ are different. Find the smallest integer $ n $ such that no valid string of length $ n $ exists.

The first line contains a single integer $ t $ ( $ 1 \le t \le 500 $ ) — the number of test cases. The first and only line of each test case contains two integers $ k $ and $ x $ ( $ 1 \le k \le 26 $ , $ 1 \le x \le 15 $ ).

For each test case, output the minimal $ n $ .

For the first test case, there are no valid strings of length $ n=3 $ . For $ n=2 $ , one such valid example is ab. Note that the only pair $ (i, j) $ that $ (j-i) $ is divisible by $ x=1 $ and $ 1 \le i < j \le n $ for $ n=2 $ is $ (1, 2) $ . For the second test case, there are no valid strings of length $ n=7 $ . For $ n=6 $ , one such valid example is aabccb. Note that all pairs $ (i, j) $ that $ (j-i) $ is divisible by $ x=2 $ and $ 1 \le i < j \le n $ for $ n=6 $ include $ (1, 3) $ , $ (1, 5) $ , $ (2, 4) $ , $ (2, 6) $ , $ (3, 5) $ , and $ (4, 6) $ . For the third test case, there are no valid strings of length $ n=6 $ . For $ n=5 $ , one such valid example is aaaaa. Note that there are no pairs $ (i, j) $ that $ (j-i) $ is divisible by $ x=5 $ and $ 1 \le i < j \le n $ for $ n=5 $ .