# Smallest integer with digit sum M and multiple of N

Given two positive integers N and M, the task is to find the smallest positive integer which is divisible by N and whose digit sum is M. Print -1 if no such integer exists within the range of int.

Examples:

```Input: N = 13, M = 32
Output: 8879
8879 is divisible by 13 and its
Sum of digits of 8879 is 8+8+7+9 = 32
i.e. equals to M

Input: N = 8, M = 32;
Output: 8888
```

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

Approach : Start with N and iterate over all the multiples of n, and check whether its digit sum is equal to m or not. This problem can be solved in logn(INT_MAX) * log10(INT_MAX) time. The efficiency of this approach can be increased by starting the iteration with a number which has at least m/9 digit.

Below is the implementation of the approach:

## C++

 `// C++ implementation of the above approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return digit sum ` `int` `digitSum(``int` `n) ` `{ ` `    ``int` `ans = 0; ` `    ``while` `(n) { ` `        ``ans += n % 10; ` `        ``n /= 10; ` `    ``} ` ` `  `    ``return` `ans; ` `} ` ` `  `// Function to find out the smallest integer ` `int` `findInt(``int` `n, ``int` `m) ` `{ ` `    ``int` `minDigit = ``floor``(m / 9); ` ` `  `    ``// Start of the iterator (Smallest multiple of n) ` `    ``int` `start = ``pow``(10, minDigit) -  ` `                ``(``int``)``pow``(10, minDigit) % n; ` ` `  `    ``while` `(start < INT_MAX) { ` `        ``if` `(digitSum(start) == m) ` `            ``return` `start; ` `        ``else` `            ``start += n; ` `    ``} ` `    ``return` `-1; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 13, m = 32; ` `    ``cout << findInt(n, m); ` `    ``return` `0; ` `} `

## Java

 `// Java implementation of the above approach  ` ` `  `class` `GFG ` `{ ` ` `  `    ``// Function to return digit sum  ` `    ``static` `int` `digitSum(``int` `n)  ` `    ``{  ` `        ``int` `ans = ``0``;  ` `        ``while` `(n != ``0``) ` `        ``{  ` `            ``ans += n % ``10``;  ` `            ``n /= ``10``;  ` `        ``}  ` `     `  `        ``return` `ans;  ` `    ``}  ` `     `  `    ``// Function to find out the  ` `    ``// smallest integer  ` `    ``static` `int` `findInt(``int` `n, ``int` `m)  ` `    ``{  ` `        ``int` `minDigit = (``int``)Math.floor((``double``)(m / ``9``));  ` `     `  `        ``// Start of the iterator (Smallest multiple of n)  ` `        ``int` `start = (``int``)Math.pow(``10``, minDigit) -  ` `                    ``(``int``)Math.pow(``10``, minDigit) % n;  ` `     `  `        ``while` `(start < Integer.MAX_VALUE)  ` `        ``{  ` `            ``if` `(digitSum(start) == m)  ` `                ``return` `start;  ` `            ``else` `                ``start += n;  ` `        ``}  ` `        ``return` `-``1``;  ` `    ``}  ` ` `  `    ``// Driver code  ` `    ``static` `public` `void` `main(String args[])  ` `    ``{  ` `        ``int` `n = ``13``, m = ``32``;  ` `        ``System.out.print(findInt(n, m));  ` `    ``}  ` `} ` ` `  `// This code is contributed  ` `// by Akanksha Rai `

## Python3

 `# Python 3 implementation of the  ` `# above approach ` `from` `math ``import` `floor, ``pow` ` `  `import` `sys ` ` `  `# Function to return digit sum ` `def` `digitSum(n): ` `    ``ans ``=` `0``; ` `    ``while` `(n): ` `        ``ans ``+``=` `n ``%` `10``; ` `        ``n ``=` `int``(n ``/` `10``); ` ` `  `    ``return` `ans ` ` `  `# Function to find out the smallest  ` `# integer ` `def` `findInt(n, m): ` `    ``minDigit ``=` `floor(m ``/` `9``) ` ` `  `    ``# Start of the iterator (Smallest  ` `    ``# multiple of n) ` `    ``start ``=` `(``int``(``pow``(``10``, minDigit)) ``-`  `             ``int``(``pow``(``10``, minDigit)) ``%` `n) ` ` `  `    ``while` `(start < sys.maxsize): ` `        ``if` `(digitSum(start) ``=``=` `m): ` `            ``return` `start ` `        ``else``: ` `            ``start ``+``=` `n ` `    ``return` `-``1` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``n ``=` `13` `    ``m ``=` `32` `    ``print``(findInt(n, m)) ` ` `  `# This code is cotributed by ` `# Surendra_Gangwar `

## C#

 `// C# implementation of the above approach  ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `    ``// Function to return digit sum  ` `    ``static` `int` `digitSum(``int` `n)  ` `    ``{  ` `        ``int` `ans = 0;  ` `        ``while` `(n != 0) ` `        ``{  ` `            ``ans += n % 10;  ` `            ``n /= 10;  ` `        ``}  ` `     `  `        ``return` `ans;  ` `    ``}  ` `     `  `    ``// Function to find out the  ` `    ``// smallest integer  ` `    ``static` `int` `findInt(``int` `n, ``int` `m)  ` `    ``{  ` `        ``int` `minDigit = (``int``)Math.Floor((``double``)(m / 9));  ` `     `  `        ``// Start of the iterator (Smallest multiple of n)  ` `        ``int` `start = (``int``)Math.Pow(10, minDigit) -  ` `                    ``(``int``)Math.Pow(10, minDigit) % n;  ` `     `  `        ``while` `(start < ``int``.MaxValue)  ` `        ``{  ` `            ``if` `(digitSum(start) == m)  ` `                ``return` `start;  ` `            ``else` `                ``start += n;  ` `        ``}  ` `        ``return` `-1;  ` `    ``}  ` ` `  `    ``// Driver code  ` `    ``static` `public` `void` `Main()  ` `    ``{  ` `        ``int` `n = 13, m = 32;  ` `        ``Console.WriteLine(findInt(n, m));  ` `    ``}  ` `} ` ` `  `// This code is contributed by Ryuga `

## PHP

 ` `

Output:

```8879
``` My Personal Notes arrow_drop_up Discovering ways to develop a plane for soaring career goals

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