Problem B. Professor Q’s Software

单点时限:1000ms

内存限制:256MB

Professor Q develops a new software. The software consists of N modules which
are numbered from 1 to N. The i-th module will be started up by signal Si. If
signal Si is generated multiple times, the i-th module will also be started
multiple times. Two different modules may be started up by the same signal.
During its lifecircle, the i-th module will generate Ki signals: E1, E2, …,
EKi. These signals may start up other modules and so on. Fortunately the
software is so carefully designed that there is no loop in the starting
chain of modules, which means eventually all the modules will be stoped.
Professor Q generates some initial signals and want to know how many times
each module is started.

The first line contains an integer T, the number of test cases. T test cases
follows.

For each test case, the first line contains contains two numbers N and M,
indicating the number of modules and number of signals that Professor Q
generates initially.

The second line contains M integers, indicating the signals that Professor Q
generates initially.

For 20% data, all N, M <= 10
For 40% data, all N, M <= 103
For 100% data, all 1 <= T <= 5, N, M <= 105, 0 <= K <= 3, 0
<= S, E <= 105.

Hint: HUGE input in this problem. Fast IO such as scanf and BufferedReader are recommended.

For each test case, output a line with N numbers Ans1, Ans2, … , AnsN. Ansi
is the number of times that the i-th module is started. In case the answers
may be too large, output the answers modulo 142857 (the remainder of division
by 142857).

样例输出