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Problem 2017 Hwh’s Problem

## Problem Description

Polynomial is an expression of more than two algebraic terms, esp. the sum of several terms that contain different powers of the same variable(s).

For example, G( p ) = 7 + 6g^1 + 2g^2 + 0g^3 + 113g^4 is an expression.

Hwh is one “SB” ( short for “ShenBen” ) and he always love math!In this problem, you are expected to calculate the coefficients of the polynomial S(g) = G(p)^m, here m is an integer larger than zero.

For example, G(p) = 3 + 2g^1 , and m = 2, then S(g) = 4g^2 + 12g + 9, so the coefficients of S(g) are {4, 12, 9}; G(p) = 3 + 2g^1 , and m = 3, then S(g) = 8g^3 + 36g^2 + 54g + 27, so the coefficients of S(g) are { 8, 36, 54, 27 }.

The coefficients may be so large, so hwh wants to know the coefficients (mod 211812353).

## Input

In the first line one integer T indicates the number of test cases. (T <= 1000)

For every case, two integers n and m in a single line, indicate the number of element of the G(p) and the value of m. (2 <= n <= 10^5, 1 <= m <= 50000, n * m <= 10^5)

Then one line has n integers Ki, indicates the i-th coefficient of G(p). (0 <= Ki <= 10^9)

## Output

For each test case, output (n – 1)*m + 1 lines, the i-th (i >= 0) line output “[i] = ci”, where ci is the coefficient of g^i in S(g)

Output one blank line after each test case.

## Sample Input

2 2 2 3 2 2 3 3 2

## Sample Output

[0] = 9 [1] = 12 [2] = 4 [0] = 27 [1] = 54 [2] = 36 [3] = 8

## Source

FOJ有奖月赛-2011年03月

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