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#include <iostream>
#include <vector>
#include <cmath>

class Solution {
public:
    int maxPathScore(std::vector<std::vector<int>>& grid, int k) {
        int m = grid.size();
        int n = grid[0].size();
        std::vector<std::vector<int>> dp(n, std::vector<int>(k + 1, -1));
        int diff = (grid[0][0] != 0);
        if (k >= diff) {
            dp[0][grid[0][0]] = grid[0][0];
        }
        else {
            return -1;
        }
        
        for (int j = 1; j < n; ++j) {
            diff = (grid[0][j] != 0);
            for (int c = diff; c <= k; ++c) {
                if (dp[j - 1][c - diff] >= 0) {
                    dp[j][c] = grid[0][j] + dp[j - 1][c - diff];
                }
                else {
                    dp[j][c] = -1;
                }
            }
        }
        
        for (int i = 1; i < m; ++i) {
            diff = (grid[i][0] != 0);
            for (int c = k; c >= diff; --c) {
                if (dp[0][c - diff] >= 0) {
                    dp[0][c] = grid[i][0] + dp[0][c - diff];
                }
                else {
                    dp[0][c] = -1;
                }
            }
            if (diff) {
                dp[0][0] = -1;
            }
            
            for (int j = 1; j < n; ++j) {
                diff = (grid[i][j] != 0);
                for (int c = k; c >= diff; --c) {
                    int prev = std::max(dp[j - 1][c - diff], dp[j][c - diff]);
                    if (prev >= 0) {
                        dp[j][c] = grid[i][j] + prev;
                    }
                    else {
                        dp[j][c] = -1;
                    }
                }
                if (diff) {
                    dp[j][0] = -1;
                }
            }
        }
        
        int res = -1;
        for (int c = 0; c <= k; ++c) {
            res = std::max(dp.back()[c], res);
        }
        return res;
    }
};