This is an \(\textbf{approximate}\) problem.

You are given 2 numbers n and m and a \(n \times n\) matrix C. Construct an array a of length n whose sum is equal to m so that the following value \(\sum_{i = 1}^{n} \sum_{j = 1}^{n} C[i][j] \cdot (a_i - a_j) ^ 2\) is minimized.

\(\textbf{Input}\)

The first line contains 2 integers - \(n,m\).

The next \((i + 1)^{th} \; (1 \le i \le n)\) line contains n integers - \(C[i][1], \; C[i][2], \; \dots \;, C[i][n] \; (C[i][i] = 0, \; C[i][j] = C[j][i])\).

There exists three types of test cases and constraints are determined for each type. Please read the "Tests" section below in order to check the constraints.

\(\textbf{Output}\)

Output n nonegative integers - \(a_1, a_2 , \dots , a_n\) \((0 \le a_i \le m)\).

The array a must satisfy the condition \(\sum_{i = 1}^{n} a_i = m\).

\(\textbf{Scoring}\)

The final score is equal to \(\sum_{i = 1}^{n} \sum_{j = 1}^{n} C[i][j] \cdot (a_i - a_j) ^ 2\).

\(\textbf{Tests}\)

There will \(99\) tests with three types of generation:

\(n = 32\) and m is chosen uniformly from interval \([4072,4088]\), \(C[i][j] \; (1 \le i < j \le n)\) is uniformly chosen from interval \([0,2^{20}]\).
\(n = 256\) and m is chosen uniformly from interval \([3841,4096]\). A permutation p is uniformly chosen and a tree is created with vertices \((p_i,p_{q_i})\) \((1 < i \le n)\) where \(q_i\) is uniformly chosen in interval \([1,i - 1]\). After this \(C[p_i][p_{q_i}]\) \((1 < i \le n)\) is uniformly chosen in interval \([0,2^{22}]\) while all other values in array C are equal to 0.
\(n = 256\) and m is chosen uniformly from interval \([3841,4096]\), \(C[i][j] \; (1 \le i < j \le n)\) is uniformly chosen from interval \([0,2^{14}]\).

After the contest, \(99\) new tests generated with a different seed will be uploaded and the solutions will be evaluated on these tests.