Implementing global sequence alignment

Question

i am going to create a needleman-wunsch global sequence alignment. But my answer is wrong. Please help me check my code. Sometimes when two sequence match, but it will still runs the mismatch function. Ignore my poor english , thanks.

#include <iostream>
using namespace std;

int max(int a , int b , int c ) ; // declaration

int main (){

  string A = "ABBC" ;
  string B = "CBAC" ;
  int a = 3 ; // match
  int b = -1 ; // mismatch
  int c = -2 ; // gap
  int i , j ;

    // calculate the string size
    int m = A.size();
    int n = B.size();

    //construct a table
    int M[m+1][n+1] = {0} ;

    //insert first row and column with gap
    for (i=0; i<=m ;i++){
        M[i][0]=i*c;
    }
    for (j=0; j<=n ;j++){
        M[0][j]=j*c;
    }

  //calculate the whole matrix
    for (j=1; j<=n ; j++){
        for (i=1 ; i<=m ; i++){
            if (A[i-1] == B[j-1]){
                M[i][j] = M[i-1][j-1] + a ;
            }else{
                M[i][j] = max(M[i-1][j-1]+b ,
                              M[i-1][j]+c ,
                              M[i][j-1]+c);
            }
        }
    }
        //PRINT
    cout << "        ";
    for(  i = 0; i <= m; i++ ){
        cout << A[i] << "   ";
    }
    cout << "\n  ";

    for(  i = 0; i <= n; i++ ){
        if( i > 0 ){
            cout << B[i-1] << " ";
       }

        for(  j = 0; j <= m; j++ ){
            cout.width( 3 );
            cout << M[i][j] << " ";
        }
        cout << endl;
    }
}

// function for maximum value
int max(int a , int b , int c ){
    if(a>b && a>c){
        return a ;
    }else if(b>a && b>c){
        return b ;
    }else {
        return c ;
    }
}

and here is my output (the highlighted is the wrong answer) :