case 9 failed: expected "000100111" got "000100000"
input:6 15
2 4 5
1 3 4
1 1 3
2 4 6
2 6 3
2 1 3
1 3 2
2 4 6
2 1 5
1 4 5
1 2 5
2 2 3
1 3 2
2 6 3
2 1 6