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*.

**Output**

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

Sample test(s)

output

qertwy
qtewry
qetyrw

Note

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