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3680.   Hello Kiki
Time Limit: 1.0 Seconds   Memory Limit: 65536K
Total Runs: 113   Accepted Runs: 35

One day I was shopping in the supermarket. There was a cashier counting coins seriously when a little kid running and singing "门前大桥下游过一群鸭,快来快来数一数,二四六七八". And then the cashier put the counted coins back morosely and count again...

Hello Kiki is such a lovely girl that she loves doing counting in a different way. For example, when she is counting X coins, she count them N times. Each time she divide the coins into several same sized groups and write down the group size Mi and the number of the remaining coins Ai on her note.

One day Kiki's father found her note and he wanted to know how much coins Kiki was counting.


The first line is T indicating the number of test cases.

Each case contains N on the first line, Mi (1 ≤ iN) on the second line, and corresponding Ai(1 ≤ iN) on the third line.

All numbers in the input and output are integers. 1 ≤ T ≤ 100, 1 ≤ N ≤ 6, 1 ≤ Mi ≤ 50, 0 ≤ Ai < Mi


For each case output the least positive integer X which Kiki was counting in the sample output format. If there is no solution then output -1.

Sample Input

14 57
5 56
19 54 40 24 80
11 2 36 20 76

Sample Output

Case 1: 341
Case 2: 5996

Author: digiter

Source: Multi-School Training Contest 2010 - BJTU Site #13
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