由给定两位数和给定数字之和构成的数字计数

//function to count the number formed by given digits whose sum having the given digit
#include <bits/stdc++.h>

using namespace std;

const int n=1000001;

const int mod=1e9+7;

//initialising array to store values of factorial and inverseFactorial till n
int fac[n]={0};
int inverseFac[n]={0};

//to calculate the inverse factorial of the last index
int lastFactorialIndex(int n,int m)
{
  int p=m;
  int a=1,b=0;
  if(m==1)
  {
      return 0;
  }
    while(n>1)
    {
      int quotient=n/m;
      
      int temp=m;
      
      m=n%m;
      
      n=temp;
      temp=b;
      
      b=a-quotient*b;
      
      a=temp;
    }

    if(a<0)
    {
     a=a+p; 
    }
	return a;
    
}

//function to store the values of factorial in the array
void factorial()
{
   fac[0]=1;
   
   fac[1]=1;
   
   for(int i=2;i<n;i++)
   {
       //since n!=n*(n-1)!
       fac[i]=(long long)fac[i-1]*i%mod;
   }
   
  
}

//function to calculate the inverse factorials for all values till n
void inverseFactorial()
{
    inverseFac[0]=1;
    inverseFac[1]=1;
    //calling the function to calculate the inverse factorial of last index
    inverseFac[n-1]=lastFactorialIndex(fac[n-1],mod);
    
    for(int i=n-2;i>=2;i--)
    {
        //inverse(i!)=inverse((i+1)!)*(i+1)
       inverseFac[i]=((long long)inverseFac[i+1]*(long long)(i+1)) % mod; 
    }
}

//function to check if the sum has only digits x and y
bool cal(int sum,int x,int y)
{

    if(sum==0)
    {
      return false;  
    }
    
    while(sum>0)
    {
        if((sum%10)!=x && (sum%10)!=y) //checking each digit of the number
        {
         return false;   
        }
        sum=sum/10;
    }
    return true;
}

//function give the number of ways of distinct numbers can be formed using i times x digit
long long int combinatorics(int n,int r)
{
    //using the formula nCr= factorial(n) * modInverse(n-r)*modInverse(r) % mod
 long long int ways= (long long)fac[n]*(long long)inverseFac[r] %mod *(long long)inverseFac[n-r]%mod;
 
  return ways;
}

// function to calculate count of numbers
int count_numbers(int m,int x,int y)
{
    //if both the digits are equal
    if(x==y)
    {
        if(cal(m*x,x,y)==true){
           return 1; 
        }
        else{
        return 0;
        }
    }
    int count=0;
    for(int i=0;i<=m;i++)
    {
        if(cal(i*x + (m-i)*y,x,y)) //checking for each possible case of x digit appearing i times
        {
           //if sum has the digits x and y, calculate the number of ways
            count = (count + combinatorics(m,i)) % mod; 
        }
        
    }
    return count;
}

int main()
{
    //calling the function to pregenerate factorials and inverse factorials
factorial();
inverseFactorial();

int m=188;
int x=8;
int y=4;
cout<<count_numbers(m,x,y);

return 0;
}