**Problem Link**

**Setter**-pavan sai kiran

**Editorial**pavan sai kiran

**DIFFICULTY**

Hard

**PREREQUISITES**

sequence and series,floyd triangle

**PROBLEM**

According to the problem,you just have to find the string ‘B’ from the given string ‘A’ and find the kth character in the string ‘B’.

**EXPLANATION**

let us take String ‘A’ as “abcd” and k be 15, so now the string ‘B’ will be

“aababcabcdbbcbcdccdd”

a a b a b c a b c d b b c b c d c c d d

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

now using only the string ‘A’ by writting the corresponding number under its corresponding letter,this can be written as:

a–b--c–d

1

2–3

4–5--6

7–8--9-10

–11

–12-13

–14-15-16

-----17

-----18-19

--------20

now certain floyd triangles are formed starting with length 4 which is the length of string ‘A’ and ending with 1.Now find the floyd triangle in which k is present.We can find that using the last terms of the floyd triangles as they from a series.In this case the series is,0,10,16,19,20.The ith term of this series is found by adding sigma(n-i-1) to the (i-1)th term where n is length of string ‘A’ and first term of this series is always 0.

k is present in the floyd triangle whose last term is greater than k. In this way the triangle is found.Now we just have to find the row in which k is present.Now take a variable ‘j’ which has value n-1 and ‘x’ which has last term of triangle.let l be be the number of lines of the required triangle that is found.Now k is present in the upper most row whose last term is greater than k.This can be achieved by subtracting l from x and decrementing j and l simultaneously.when x is less than k,then the row below is required.now the required answer is just printing j-k-1 index of string ‘A’.