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Chef is attending a chess competition. There are n people take part in. Each pair of people compete once. Winner earns 1 point, loser earns 0 point. A game never ends with a draw. After all games are over, Organizer decide to award prize to each participant. The prize of each participant is the square of his points. What is all possible total money the organizer will pay for all participants? Given k, determine if there is at least one scenario that the total money the organizers will pay is exactly k? If there's any, output one of them.
First line contains an integer T denotes the number of test cases. The T following lines, each line contains two integers n, k.
For each test case, if there isn't a such scenario, output -1.
otherwise print n lines, each line contains n characters. j-th character in i-th line is "1" if i-th participant wins j-th participant, otherwise "0". (i-th character in i-th line is always "0")
- 1 ≤ T ≤ 100
- 1 ≤ n ≤ 103
- The sum of n over all test cases is at most 104
- 1 ≤ k ≤ 109
- Subtask #1 (10 points): n ≤ 5
- Subtask #2 (30 points): n ≤ 50
- Subtask #3 (60 points): original constrains
Input: 3 2 1 3 6 4 10 Output: 01 00 -1 0100 0011 1001 1000
|Tags||chemthan, constructive, ltime53, medium-hard|
|Time Limit:||1 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, PYP3, CLOJ, FS|
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