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A Mysterious Function
Time Limit: 1000MSMemory Limit: 65536K
Total Submissions: 3914Accepted: 2713

Description

For any integers p and q with q > 0, define p mod q to be the integer r with 0 <= r <= q āˆ’1 such that pāˆ’r is divisible by q. For example, we have
    109 mod 10 = 9
    āˆ’7 mod 3 = 2
    āˆ’56 mod 7 = 0

Let Φ be a function defined recursively as follows.

where a, b, c, d, e, f, g, h are integers with 0 < a, b, c, d, e, f, g, h <= 1000. One can easily see that 0 <= Φ(i) <= 1000 holds for any integer i >= 0. Now for any given integers a, b, c, d, e, f, g, h, i with 0 < a, b, c, d, e, f, g, h, i <= 1000, you are asked to write a program to output

Φ(i). (Hint: a direct recursive implementation of the above recurrence

relation is likely to run forever for large i.)

Input

The first line contains the number n of test cases. Each of the following n lines contains the sequence a, b, c, d, e, f, g, h, i of integers.

Output

For each test case, your program has to output the correct value of Φ(i).

Sample Input

3
1 2 3 4 5 6 7 8 9
11 12 13 14 15 16 17 18 19
321 322 323 324 325 326 327 328 329

Sample Output

4
0
90

Source

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