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Find M-th number whose repeated sum of digits of a number is N
• Last Updated : 08 Feb, 2019

Given two positive integers N and M. The task is to find M-th number whose sum of digits of a number until sum becomes single digit is N.

Examples:

```Input: N = 1, M = 3
Output: 19
The first two numbers being 1 and 9.

Input: N = 2, M = 5
Output:  38
The first four numbers being 2, 11, 20 and 29.
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

A naive approach is to iterate for all numbers and keep a count of number whose sum returns N.

An efficient approach is to find the summation of digits till it becomes single digits in O(1) that has been discussed here. Hence the formula to find M-th number will be:

Mth number: (M-1)*9 + N

Below is the implementation of the above approach:

## C++

 `// C++ program to Find m-th number whose``// sum of digits of a number until``// sum becomes single digit is N``#include ``using` `namespace` `std;`` ` `// Function to find the M-th``// number whosesum till one digit is N``int` `findNumber(``int` `n, ``int` `m)``{``    ``int` `num = (m - 1) * 9 + n;``    ``return` `num;``}`` ` `// Driver Code``int` `main()``{`` ` `    ``int` `n = 2, m = 5;``    ``cout << findNumber(n, m);``    ``return` `0;``}`

## Java

 `// Java program to Find m-th number whose``// sum of digits of a number until``// sum becomes single digit is N``class` `GFG``{`` ` `// Function to find the M-th``// number whosesum till one digit is N``static` `int` `findNumber(``int` `n, ``int` `m)``{``    ``int` `num = (m - ``1``) * ``9` `+ n;``    ``return` `num;``}`` ` `// Driver Code``public` `static` `void` `main(String args[])``{``    ``int` `n = ``2``, m = ``5``;``    ``System.out.print(findNumber(n, m));``}``}`` ` `// This code is contributed``// by Akanksha Rai`

## Python3

 `# Python3 program to Find m-th number ``# whose sum of digits of a number``# until sum becomes single digit is N `` ` `# Function to find the M-th ``# number whosesum till one digit is N``def` `findNumber(n, m) :``     ` `    ``num ``=` `(m ``-` `1``) ``*` `9` `+` `n; ``    ``return` `num; `` ` `# Driver Code ``if` `__name__ ``=``=` `"__main__"` `: `` ` `    ``n ``=` `2` `;``    ``m ``=` `5` `; ``    ``print``(findNumber(n, m))``     ` `# This code is contributed by Ryuga`

## C#

 `// C# program to Find m-th number whose``// sum of digits of a number until``// sum becomes single digit is N``using` `System;`` ` `class` `GFG``{`` ` `// Function to find the M-th``// number whosesum till one digit is N``static` `int` `findNumber(``int` `n, ``int` `m)``{``    ``int` `num = (m - 1) * 9 + n;``    ``return` `num;``}`` ` `// Driver Code``public` `static` `void` `Main()``{``    ``int` `n = 2, m = 5;``    ``Console.Write(findNumber(n, m));``}``}`` ` `// This code is contributed``// by Akanksha Rai`

## PHP

 ``
Output:
```38
```

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