# Find Nth smallest number that is divisible by 100 exactly K times

Given two numbers N and K . The task is to find N’th smallest number that is divided by 100 exactly K times.

**Examples:**

Input :N = 12, K = 2

Output :120000

120000 is divisible by 100 exactly 2 times and

is the 12 th smallest number also.

Input :N = 1000, K = 2

Output :10010000

**Approach:**

- First find the smallest number that is divisible by 100 exactly K times. That is 2*K 0’s after 1 as 100 has two 0’s only.
- To find N’th smallest number, multiply N with the previous number we get after adding 2*k 0’s.
- Consider a case when N is divisible by 100 as if we multiply N with the previous number then the new number will have more than (2*k + 1) trailing 0’s that means it will divisible by 100 more than K times.
- Multiply that number with (N + 1). Use string as N and K can be very large that will not fit in integer limit.

Below is the implementation of above approach:

## C++

`// C++ implementation of above approach ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to find the Nth smallest number ` `string find_number(` `int` `N, ` `int` `K) ` `{ ` ` ` `string r; ` ` ` ` ` `// If N is divisible by 100 then we ` ` ` `// multiply N + 1 otherwise, it will be ` ` ` `// divisible by 100 more than K times ` ` ` `if` `(N % 100 == 0) { ` ` ` `N += 1; ` ` ` ` ` `// convert integer to string ` ` ` `r = to_string(N); ` ` ` `} ` ` ` ` ` `// if N is not divisible by 100 ` ` ` `else` `{ ` ` ` `// convert integer to string ` ` ` `r = to_string(N); ` ` ` `} ` ` ` ` ` `// add 2*K 0's at the end to be divisible ` ` ` `// by 100 exactly K times ` ` ` `for` `(` `int` `i = 1; i <= K; i++) ` ` ` `r += ` `"00"` `; ` ` ` ` ` `return` `r; ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` `int` `N = 1000, K = 2; ` ` ` `string ans = find_number(N, K); ` ` ` `cout << ans << ` `"\n"` `; ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java implementation of above approach ` `import` `java.util.*; ` ` ` `class` `GFG ` `{ ` ` ` `// Function to find the Nth smallest number ` `static` `String find_number(` `int` `N, ` `int` `K) ` `{ ` ` ` `String r; ` ` ` ` ` `// If N is divisible by 100 then we ` ` ` `// multiply N + 1 otherwise, it will be ` ` ` `// divisible by 100 more than K times ` ` ` `if` `(N % ` `100` `== ` `0` `) ` ` ` `{ ` ` ` `N += ` `1` `; ` ` ` ` ` `// convert integer to string ` ` ` `r = String.valueOf(N); ` ` ` `} ` ` ` ` ` `// if N is not divisible by 100 ` ` ` `else` ` ` `{ ` ` ` `// convert integer to string ` ` ` `r = String.valueOf(N); ` ` ` `} ` ` ` ` ` `// add 2*K 0's at the end to be divisible ` ` ` `// by 100 exactly K times ` ` ` `for` `(` `int` `i = ` `1` `; i <= K; i++) ` ` ` `r += ` `"00"` `; ` ` ` ` ` `return` `r; ` `} ` ` ` `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ` `int` `N = ` `1000` `, K = ` `2` `; ` ` ` `String ans = find_number(N, K); ` ` ` `System.out.println(ans); ` `} ` `} ` ` ` `/* This code is contributed by PrinciRaj1992 */` |

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## Python3

`# Python3 implementation of above approach ` ` ` `# Function to find the Nth smallest number ` `def` `find_number(N, K): ` ` ` ` ` `r ` `=` `"" ` ` ` ` ` `# If N is divisible by 100 then we ` ` ` `# multiply N + 1 otherwise, it will be ` ` ` `# divisible by 100 more than K times ` ` ` `if` `(N ` `%` `100` `=` `=` `0` `): ` ` ` `N ` `+` `=` `1` `; ` ` ` ` ` `# convert integer to string ` ` ` `r ` `=` `str` `(N) ` ` ` ` ` `# if N is not divisible by 100 ` ` ` `else` `: ` ` ` ` ` `# convert integer to string ` ` ` `r ` `=` `str` `(N) ` ` ` ` ` `# add 2*K 0's at the end to be divisible ` ` ` `# by 100 exactly K times ` ` ` `for` `i ` `in` `range` `(` `1` `, K ` `+` `1` `): ` ` ` `r ` `+` `=` `"00"` ` ` ` ` `return` `r ` ` ` `# Driver Code ` `N ` `=` `1000` `K ` `=` `2` `; ` `ans ` `=` `find_number(N, K) ` `print` `(ans) ` ` ` `# This code is contributed by Mohit Kumar ` |

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**Output:**

10010000

**Time Complexity: **O(K)

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