Find the length of the longest path in the matrix with the consecutive character along with its path

Given M * N matrix of characters, find the length of the longest path in the matrix starting from the given source.

Note : All characters in the longest path should be increasing and consecutive to each other in alphabetical order. We are allowed to search the next character in all 8 directions.

I have correctly found out the length of the sequence but there is a problem in path. path is not correct.
Here is my code

#include<iostream>
#include<vector>
using namespace std;

//Below array details all 8 posible directions
int row[] = { -1,-1,-1, 0, 0, 1, 1, 1 };
int col[] = { 1, 0, -1, 1,-1, -1,0, 1 };


int length(char arr[][5], int x, int y, char previous, vector<pair<int,int> > &path, int k)
{
    // x and y must be bounded between 0 to 4
    if( x < 0  || x > 4 || y > 4 || y < 0)
       return 0;

    int l = 0;
    int max_length = 0;

    for( int i = 0; i < 8; i++)
    {
        // storing next character in search
        char ch = arr[x+row[i]][y+col[i]];

        //checking whether ch is the next character in the sequence or not
        if(ch == previous + 1)
        {  
            //if k != path.size() then we have taken back in
            // the sequence so no need to push back character in the path
            if(k == path.size())
              {
                // Pushing co-ordinates of next valid character
                path.push_back(make_pair(x+row[i], y+col[i]));
              }
            else
                path.pop_back();

            l = 1 + length(arr, x+row[i], y+ col[i], ch , path, ++k);
            max_length = max( l, max_length);
        }

    }

    return max_length;
}

int main()
{
    char arr[5][5] = { 
                      { 'd','e','h','x','b'},
                      { 'a','o','g','p','e'},
                      { 'd','d','c','f','d'},
                      { 'e','b','e','a','s'},
                      { 'c','d','y','e','n'}
                    };
    vector<pair<int,int> > path;

    //Pusing source address
    path.push_back(make_pair(2,2));

    int k = 1;

    int Len = length(arr, 2, 2 , arr[2][2], path, k);

    cout << "Length of the Longest sequence is : " << Len + 1 <<endl; 

    //printing the path
    cout << "Path is : "<<endl;
    for( pair<int,int> i : path)
    {
        cout <<"( " << i.first <<","<<i.second <<" )" ;
    }

    return 0;
}

Actual output :

Length of the Longest sequence is : 6
Path is
( 2,2 )( 2,1)( 3,0 )( 3,2 )( 2,3 )( 1,2 )( 0,2 )

Expected output

Length of the Longest sequence is : 6
Path is
( 2,2 )(2,1 )( 3,2 )( 2,3 )( 1,2 )( 0,2 )

There is a extra (3,0) in my output. When I take back from (3,0) , I could not pop it.
Any help will be appreciated.