B'You have received your birthday gifts -- n triples of integers! The i -th of them is lbrace a_{i}, b_{i}, c_{i} rbrace . All numbers are greater than or equal to 0 , and strictly smaller than 2^{k} , where k is a fixed integer. One day, you felt tired playing with triples. So you came up with three new integers x , y , z , and then formed n arrays. The i -th array consists of a_i repeated x times, b_i repeated y times and c_i repeated z times. Thus, each array has length (x + y + z) . You want to choose exactly one integer from each array such that the XOR (bitwise exclusive or) of them is equal to t . Output the number of ways to choose the numbers for each t between 0 and 2^{k} - 1 , inclusive, modulo 998244353 . The first line contains two integers n and k ( 1 <= q n <= q 10^{5} , 1 <= q k <= q 17 ) -- the number of arrays and the binary length of all numbers. The second line contains three integers x , y , z ( 0 <= q x,y,z <= q 10^{9} ) -- the integers you chose. Then n lines follow. The i -th of them contains three integers a_{i} , b_{i} and c_{i} ( 0 <= q a_{i} , b_{i} , c_{i} <= q 2^{k} - 1 ) -- the integers forming the i -th array. Print a single line containing 2^{k} integers. The i -th of them should be the number of ways to choose exactly one integer from each array so that their XOR is equal to t = i-1 modulo 998244353 . In the first example, the array we formed is (1, 0, 0, 1, 1, 1) , we have two choices to get 0 as the XOR and four choices to get 1 . In the second example, two arrays are (0, 1, 1, 2) and (1, 2, 2, 3) . There are sixteen (4 cdot 4) choices in total, 4 of them ( 1 oplus 1 and 2 oplus 2 , two options for each) give 0 , 2 of them ( 0 '...