Generators
Little Roman is studying linear congruential generators - one of the oldest and best known pseudo-random number generator algorithms. Linear congruential generator (LCG) starts with a non-negativeinteger number x[0] also known as seed and produces an infinite sequence of non-negative integer numbers x[i] (0 ≤ x[i] < c) which are given by the following recurrence relation:
x[i+1] = (a *x[i] + b) mod c
here a, b and c are non-negative integer numbers and 0 ≤ x[0] < c.
Roman is curious about relations between sequences generated by different LCGs. In particular, he hasn different LCGs with parameters a^j, b^j and c^j for 1 ≤ j ≤ n, where the j-th LCG is generating a sequence x^j[i]. He wants to pick one number from each of the sequences generated by each LCG so that the sum of the numbers is the maximum one, but is not divisible by the given integer number k. Formally, Roman wants to find integer numbers t[j] ≥ 0 for 1 ≤ j ≤ n to maximize
subject to constraint that s mod k ≠ 0.
Input
The first line contains two integer numbers n and k (1 ≤ n ≤ 10 000, 1 ≤ k ≤ 10^9). The following n lines describe LCGs. Each line contains four integer numbers x^j[0] , a^j, b^j and c^j (0 ≤ a^j, b^j ≤ 1000, 0 ≤ x^j[0] < c^j ≤ 1000).
Output
If Roman’s problem has a solution, then write on the first line a single integer s - the maximum sum not divisible by k, followed on the next line by n integer numbers t[j] (0 ≤ t[j] ≤ 10^9) specifying some solution with this sum.
Otherwise, write to the output a single line with the number -1.