{"raw_statement":[{"iden":"statement","content":"Your team was exploring an ancient city. Suddenly you found an old scroll with 2 integer numbers N and K, which encrypts the secret code to open a treasure box. Considering a transformation on an integer X described as follows:\n\nX = X + X mod 100,\n\nthe secret code can be obtained by applying the above-described transformation K times successively to N.\n\nThe input file consists of several datasets. The first line of the input file contains the number of datasets which is a positive integer and is not greater than 500. \n\nEach dataset has two space-separated positive integers N and K (1 ≤ N ≤ 109, 1 ≤ K ≤ 109) written on a single line.\n\nFor each dataset, write on a single line the secret number decrypted from N and K.\n\n"},{"iden":"input","content":"The input file consists of several datasets. The first line of the input file contains the number of datasets which is a positive integer and is not greater than 500. Each dataset has two space-separated positive integers N and K (1 ≤ N ≤ 109, 1 ≤ K ≤ 109) written on a single line."},{"iden":"output","content":"For each dataset, write on a single line the secret number decrypted from N and K."},{"iden":"examples","content":"Input231102014 210101 10Output3110205610324"}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ t \\in \\mathbb{Z} $ be the number of datasets.  \nLet $ D = \\{(N_j, K_j) \\mid j \\in \\{1, \\dots, t\\}\\} $ be the set of datasets, where for each $ j $:  \n- $ N_j \\in \\mathbb{Z}^+ $ is the initial integer.  \n- $ K_j \\in \\mathbb{Z}^+ $ is the number of transformations.  \n\n**Constraints**  \n1. $ 1 \\le t \\le 500 $  \n2. For each $ j \\in \\{1, \\dots, t\\} $:  \n   - $ 1 \\le N_j \\le 10^9 $  \n   - $ 1 \\le K_j \\le 10^9 $  \n\n**Objective**  \nFor each dataset $ j $, define the transformation $ f(x) = x + (x \\bmod 100) $.  \nCompute the result after $ K_j $ applications:  \n$$\nR_j = f^{K_j}(N_j)\n$$  \nwhere $ f^k $ denotes the $ k $-fold composition of $ f $.","simple_statement":"Start with number N. Apply this operation K times: N = N + (N mod 100). Print the final result.","has_page_source":false}