Competitions

# Азербайджан - подготовка. Март 18

# Fibonacci Strings

Fibonacci sequence of strings is defined as follows: `s`

= _{1}**b**, `s`

= _{2}**a**, `s`

= _{k}`s`

+ _{k-1}`s`

for _{k-2}**k** > **2**. For example, `s`

= _{3}**ab**, `s`

= _{4}**aba**, `s`

= _{5}**abaab** and etc.

Given positive integers **n**, **m**, **l**. Print the substring of `s`

which starts at position _{n}**m** and have the length **l**.

#### Input

One line contains three space-separated positive integers **n**, **m** and **l**, where **1** ≤ **n** ≤ **40**; **1** ≤ **m** ≤ **length**(`S`

), _{n}**1** ≤ **l** ≤ **1000**.

#### Output

Print the substring of `s`

which starts at position _{n}**m** and have the length **l** (the length of the printed substring may be less if the length of the remainder of the string `s`

, starting from position _{n}**m**, is less than **l**).

Input example #1

5 3 2

Output example #1

aa

Input example #2

5 3 10

Output example #2

aab