Dijkstra-DP atmost K zeroing weights

#include<bits/stdc++.h>
using namespace std;
#define ar array<int,3>
int main(){
    int n,m,k;
    cin>>n>>m>>k;
    vector<vector<pair<int, int>>> adj(n);
    for(int i=0;i<m;i++){
        int u, v, w;
        cin>>u>>v>>w;
        adj[u-1].push_back({v-1, w});
        adj[v-1].push_back({u-1, w});
    }
    vector<vector<int>> dp(n, vector<int>(k + 1, INT_MAX)); //dp[i][j] -> 0 to i with atmost j skips
priority_queue<ar, vector<ar>, greater<ar>> q; // {dist,node,used}
        q.push({0, 0, 0});
        dp[0][0] = 0 ;
        while(!q.empty()){
            auto [d,n,next] = q.top();
            q.pop();
            if(d!=dp[n][next]) continue;
            if(n==0) dp[n][next]=0;
            for(auto [v,w]:adj[n]){
                if(dp[n][next]+w<dp[v][next]){
                    dp[v][next] = dp[n][next]+w;
                    q.push({dp[v][next],v,next});
                }
                if(next == k) continue;
                if(dp[n][next]<dp[v][next+1]){
                    dp[v][next+1] = dp[n][next];
                    q.push({dp[v][next+1],v,next+1});
                }
            }
        }
    for(int i = 0;i < n;i++){
        cout<<dp[i][k]<<" ";
    }
    cout<<endl;

}