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:

1. $n = 32$ and m is chosen uniformly from interval $[4072,4088]$, $C[i][j] \; (1 \le i < j \le n)$ is uniformly chosen from interval $[0,2^{20}]$.

2. $n = 256$ 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.

3. $n = 256$ 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.