Strange Sorting

题意翻译

对一个长度至少为 $d$ 的字符串（下标从0开始），定义 $d-sorting$ 的排序方式为，循环 $i$ 从 $0$ 到 $(d-1)$，将字符串中下标 $MOD\ d$ 为 $i$ 的字符按原顺序取出来依次加到末尾。\ 例：$abcde$ 的 $2-sorting$ 结果为 $acebd$。\ 给定长度为 $n$ 的字符串，$m$ 次操作，每次将所有长度为 $k$ 的子串按左到右的顺序进行一次 $d-sorting$，每次操作后输出当前串，每次操作在上一次的基础上进行。

题目描述

How many specific orders do you know? Ascending order, descending order, order of ascending length, order of ascending polar angle... Let's have a look at another specific order: $ d $ -sorting. This sorting is applied to the strings of length at least $ d $ , where $ d $ is some positive integer. The characters of the string are sorted in following manner: first come all the 0-th characters of the initial string, then the 1-st ones, then the 2-nd ones and so on, in the end go all the $ (d-1) $ -th characters of the initial string. By the $ i $ -th characters we mean all the character whose positions are exactly $ i $ modulo $ d $ . If two characters stand on the positions with the same remainder of integer division by $ d $ , their relative order after the sorting shouldn't be changed. The string is zero-indexed. For example, for string 'qwerty': Its 1-sorting is the string 'qwerty' (all characters stand on 0 positions), Its 2-sorting is the string 'qetwry' (characters 'q', 'e' and 't' stand on 0 positions and characters 'w', 'r' and 'y' are on 1 positions), Its 3-sorting is the string 'qrwtey' (characters 'q' and 'r' stand on 0 positions, characters 'w' and 't' stand on 1 positions and characters 'e' and 'y' stand on 2 positions), Its 4-sorting is the string 'qtwyer', Its 5-sorting is the string 'qywert'. You are given string $ S $ of length $ n $ and $ m $ shuffling operations of this string. Each shuffling operation accepts two integer arguments $ k $ and $ d $ and transforms string $ S $ as follows. For each $ i $ from $ 0 $ to $ n-k $ in the increasing order we apply the operation of $ d $ -sorting to the substring $ S\[i..i+k-1\] $ . Here $ S\[a..b\] $ represents a substring that consists of characters on positions from $ a $ to $ b $ inclusive. After each shuffling operation you need to print string $ S $ .

输入输出格式

输入格式

The first line of the input contains a non-empty string $ S $ of length $ n $ , consisting of lowercase and uppercase English letters and digits from 0 to 9. The second line of the input contains integer $ m $ – the number of shuffling operations ( $ 1<=m·n<=10^{6} $ ). Following $ m $ lines contain the descriptions of the operations consisting of two integers $ k $ and $ d $ ( $ 1<=d<=k<=n $ ).

输出格式

After each operation print the current state of string $ S $ .

输入输出样例

输入样例 #1

qwerty
3
4 2
6 3
5 2

输出样例 #1

qertwy
qtewry
qetyrw

说明

Here is detailed explanation of the sample. The first modification is executed with arguments $ k=4 $ , $ d=2 $ . That means that you need to apply 2-sorting for each substring of length 4 one by one moving from the left to the right. The string will transform in the following manner: qwerty $ → $ qewrty $ → $ qerwty $ → $ qertwy Thus, string $ S $ equals 'qertwy' at the end of first query. The second modification is executed with arguments $ k=6 $ , $ d=3 $ . As a result of this operation the whole string $ S $ is replaced by its 3-sorting: qertwy $ → $ qtewry The third modification is executed with arguments $ k=5 $ , $ d=2 $ . qtewry $ → $ qertwy $ → $ qetyrw