Count of all possible values of X such that A % X = B

Given two integers A and B. The task is to find the count of all possible values X such that A % X = B. If there are infinite number of possible values then print -1.

Examples:

Input: A = 21, B = 5
Output: 2
8 and 16 are the only valid values for X.

Input: A = 5, B = 5
Output: -1
X can have any value > 5

Approach: There are three possible cases:



  1. If A < B then no value of X can satisfy the given condition.
  2. If A = B then infinite solutions are possible. So, print -1 as X can be any value greater than A.
  3. If A > B then the number of divisors of (A – B) which are greater than B is the required count.

Below is the implementation of the above approach:

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the count
// of all possible values for x
// such that (A % x) = B
int countX(int a, int b)
{
    // Case 1
    if (b > a)
        return 0;
  
    // Case 2
    else if (a == b)
        return -1;
  
    // Case 3
    else {
        int x = a - b, ans = 0;
  
        // Find the number of divisors of x
        // which are greater than b
        for (int i = 1; i * i <= x; i++) {
            if (x % i == 0) {
                int d1 = i, d2 = b - 1;
                if (i * i != x)
                    d2 = x / i;
                if (d1 > b)
                    ans++;
                if (d2 > b)
                    ans++;
            }
        }
        return ans;
    }
}
  
// Driver code
int main()
{
    int a = 21, b = 5;
  
    cout << countX(a, b);
  
    return 0;
}
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// Java implementation of the approach
class GFG
{
      
    // Function to return the count 
    // of all possible values for x 
    // such that (A % x) = B 
    static int countX(int a, int b) 
    
        // Case 1 
        if (b > a) 
            return 0
      
        // Case 2 
        else if (a == b) 
            return -1
      
        // Case 3 
        else
        
            int x = a - b, ans = 0
      
            // Find the number of divisors of x 
            // which are greater than b 
            for (int i = 1; i * i <= x; i++)
            
                if (x % i == 0)
                
                    int d1 = i, d2 = b - 1
                    if (i * i != x) 
                        d2 = x / i; 
                    if (d1 > b) 
                        ans++; 
                    if (d2 > b) 
                        ans++; 
                
            
            return ans; 
        
    
  
    // Driver code 
    static public void main (String args[]) 
    
        int a = 21, b = 5
      
        System.out.println(countX(a, b)); 
      
    
}
  
// This code is contributed by AnkitRai01
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# Python 3 implementation of the approach
  
# Function to return the count
# of all possible values for x
# such that (A % x) = B
def countX( a, b):
    # Case 1
    if (b > a):
        return 0
  
    # Case 2
    elif (a == b):
        return -1
  
    # Case 3
    else:
        x = a - b
        ans = 0
  
        # Find the number of divisors of x
        # which are greater than b
        i = 1
        while i * i <= x:
            if (x % i == 0):
                d1 = i
                d2 = b - 1
                if (i * i != x):
                    d2 = x // i
                if (d1 > b):
                    ans+=1
                if (d2 > b):
                    ans+=1
            i+=1
        return ans
  
# Driver code
if __name__ == "__main__":
    a = 21
    b = 5
  
    print(countX(a, b))
      
    # This code is contributed by ChitraNayal
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// C# implementation of the approach
using System;
  
class GFG
{
      
    // Function to return the count 
    // of all possible values for x 
    // such that (A % x) = B 
    static int countX(int a, int b) 
    
        // Case 1 
        if (b > a) 
            return 0; 
      
        // Case 2 
        else if (a == b) 
            return -1; 
      
        // Case 3 
        else
        
            int x = a - b, ans = 0; 
      
            // Find the number of divisors of x 
            // which are greater than b 
            for (int i = 1; i * i <= x; i++)
            
                if (x % i == 0)
                
                    int d1 = i, d2 = b - 1; 
                    if (i * i != x) 
                        d2 = x / i; 
                    if (d1 > b) 
                        ans++; 
                    if (d2 > b) 
                        ans++; 
                
            
            return ans; 
        
    
  
    // Driver code 
    static public void Main () 
    
        int a = 21, b = 5; 
      
        Console.WriteLine(countX(a, b)); 
      
    
}
  
// This code is contributed by anuj_67..
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Output:
2




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