Migrated from Lutece 473 Hello Kiki

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Description

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 $M_i$ and the number of the remaining coins $A_i$ on her note.

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

Input

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

Each case contains $N$ on the first line, $M_i$($1\leq i \leq N$) on the second line, and corresponding $A_i$($1\leq i\leq N$) on the third line.

All numbers in the input and output are integers.

$1 \leq T \leq 100$, $1 \leq N \leq 6$, $0 \leq A_i < M_i$

Output

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 $-1$.

Samples

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

Case 1: 341
Case 2: 5996

Resources

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