There is a one-dimensional cellular automaton consisting of \textbf{N} cells. Cells are numbered from \textbf{0} to \textbf{N-1}. Each cell has a state represented as a non-negative integer less than \textbf{M}. The states of cells evolve through discrete time steps. We denote the state of the \textbf{i}-th cell at time \textbf{t} as \textbf{S(i, t)}. The state at time \textbf{t+1} is de ned by the equation \textbf{S(i, t+1) = (A × S(i-1, t) + B × S(i, t) + C × S(i+1, t))mod M}, (1) where \textbf{A}, \textbf{B} and \textbf{C} are non-negative integer constants. For \textbf{i} < \textbf{0} or \textbf{N} ≤ \textbf{i}, we de ne \textbf{S(i, t) = 0}. Given an automaton de nition and initial states of cells, your mission is to write a program that computes the states of the cells at a speci ed time \textbf{T}. \InputFile The input is a sequence of datasets. Each dataset is formatted as follows. \textbf{N M A B C T} \textbf{S(0, 0) S(1, 0) ... S(N-1, 0)} The first line of a dataset consists of six integers, namely \textbf{N}, \textbf{M}, \textbf{A}, \textbf{B}, \textbf{C} and \textbf{T}. \textbf{N} is the number of cells. \textbf{M} is the modulus in the equation (1). \textbf{A}, \textbf{B} and \textbf{C} are coefficients in the equation (1). Finally, \textbf{T} is the time for which you should compute the states. You may assume that \textbf{0} < \textbf{N} ≤ \textbf{50}, \textbf{0} < \textbf{M} ≤ \textbf{1000}, \textbf{0} ≤ \textbf{A}, \textbf{B}, \textbf{C} < \textbf{M} and \textbf{0} ≤ \textbf{T} ≤ \textbf{10^9}. The second line consists of \textbf{N} integers, each of which is non-negative and less than \textbf{M}. They represent the states of the cells at time zero. A line containing six zeros indicates the end of the input. \OutputFile For each dataset, output a line that contains the states of the cells at time \textbf{T}. The format of the output is as follows. \textbf{S(0, T) S(1, T) ... S(N-1, T)} Each state must be represented as an integer and the integers must be separated by a space.