# Count of pairs satisfying the given condition

Given two integers A and B, the task is to calculate the number of pairs (a, b) such that 1 ≤ a ≤ A, 1 ≤ b ≤ B and the equation (a * b) + a + b = concat(a, b) is true where conc(a, b) is the concatenation of a and b (for example, conc(12, 23) = 1223, conc(100, 11) = 10011). Note that a and b should not contain any leading zeroes.

Examples:

Input: A = 1, B = 12
Output: 1
There exists only one pair (1, 9) satisfying
the equation ((1 * 9) + 1 + 9 = 19)

Input: A = 2, B = 8
Output: 0
There doesn’t exist any pair satisfying the equation.

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

Approach: It can be observed that the above (a * b + a + b = conc(a, b)) will only be satisfied when the digits of an integer ≤ b contains only 9. Simply, calculate the number of digits (≤ b) containing only 9 and multiply with the integer a.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the number of ` `// pairs satisfying the equation ` `int` `countPair(``int` `a, ``int` `b) ` `{ ` `    ``// Converting integer b to string ` `    ``// by using to_string function ` `    ``string s = to_string(b); ` ` `  `    ``// Loop to check if all the digits ` `    ``// of b are 9 or not ` `    ``int` `i; ` `    ``for` `(i = 0; i < s.length(); i++) { ` ` `  `        ``// If '9' doesn't appear ` `        ``// then break the loop ` `        ``if` `(s[i] != ``'9'``) ` `            ``break``; ` `    ``} ` ` `  `    ``int` `result; ` ` `  `    ``// If all the digits of b contain 9 ` `    ``// then multiply a with string length ` `    ``// else multiply a with string length - 1 ` `    ``if` `(i == s.length()) ` `        ``result = a * s.length(); ` `    ``else` `        ``result = a * (s.length() - 1); ` ` `  `    ``// Return the number of pairs ` `    ``return` `result; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `a = 5, b = 101; ` ` `  `    ``cout << countPair(a, b); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `class` `GFG ` `{ ` ` `  `// Function to return the number of ` `// pairs satisfying the equation ` `static` `int` `countPair(``int` `a, ``int` `b) ` `{ ` `    ``// Converting integer b to String ` `    ``// by using to_String function ` `    ``String s = String.valueOf(b); ` ` `  `    ``// Loop to check if all the digits ` `    ``// of b are 9 or not ` `    ``int` `i; ` `    ``for` `(i = ``0``; i < s.length(); i++) ` `    ``{ ` ` `  `        ``// If '9' doesn't appear ` `        ``// then break the loop ` `        ``if` `(s.charAt(i) != ``'9'``) ` `            ``break``; ` `    ``} ` ` `  `    ``int` `result; ` ` `  `    ``// If all the digits of b contain 9 ` `    ``// then multiply a with String length ` `    ``// else multiply a with String length - 1 ` `    ``if` `(i == s.length()) ` `        ``result = a * s.length(); ` `    ``else` `        ``result = a * (s.length() - ``1``); ` ` `  `    ``// Return the number of pairs ` `    ``return` `result; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `a = ``5``, b = ``101``; ` ` `  `    ``System.out.print(countPair(a, b)); ` `} ` `} ` ` `  `// This code is contributed by PrinciRaj1992 `

## Python

 `# Python3 implementation of the approach ` ` `  `# Function to return the number of ` `# pairs satisfying the equation ` `def` `countPair(a, b): ` `     `  `    ``# Converting integer b to string ` `    ``# by using to_function ` `    ``s ``=` `str``(b) ` ` `  `    ``# Loop to check if all the digits ` `    ``# of b are 9 or not ` `    ``i ``=` `0` `    ``while` `i < (``len``(s)): ` ` `  `        ``# If '9' doesn't appear ` `        ``# then break the loop ` `        ``if` `(s[i] !``=` `'9'``): ` `            ``break` `        ``i ``+``=` `1` ` `  `    ``result ``=` `0` ` `  `    ``# If all the digits of b contain 9 ` `    ``# then multiply a with length ` `    ``# else multiply a with length - 1 ` `    ``if` `(i ``=``=` `len``(s)): ` `        ``result ``=` `a ``*` `len``(s) ` `    ``else``: ` `        ``result ``=` `a ``*` `(``len``(s) ``-` `1``) ` ` `  `    ``# Return the number of pairs ` `    ``return` `result ` ` `  `# Driver code ` `a ``=` `5` `b ``=` `101` ` `  `print``(countPair(a, b)) ` ` `  `# This code is contributed by mohit kumar 29 `

## C#

 `// C# implementation of the approach ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to return the number of ` `// pairs satisfying the equation ` `static` `int` `countPair(``int` `a, ``int` `b) ` `{ ` `    ``// Converting integer b to String ` `    ``// by using to_String function ` `    ``String s = String.Join(``""``, b); ` ` `  `    ``// Loop to check if all the digits ` `    ``// of b are 9 or not ` `    ``int` `i; ` `    ``for` `(i = 0; i < s.Length; i++) ` `    ``{ ` ` `  `        ``// If '9' doesn't appear ` `        ``// then break the loop ` `        ``if` `(s[i] != ``'9'``) ` `            ``break``; ` `    ``} ` ` `  `    ``int` `result; ` ` `  `    ``// If all the digits of b contain 9 ` `    ``// then multiply a with String length ` `    ``// else multiply a with String length - 1 ` `    ``if` `(i == s.Length) ` `        ``result = a * s.Length; ` `    ``else` `        ``result = a * (s.Length - 1); ` ` `  `    ``// Return the number of pairs ` `    ``return` `result; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int` `a = 5, b = 101; ` ` `  `    ``Console.Write(countPair(a, b)); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

Output:

```10
```

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