using System;
using System.Collections.Generic;
using System.Linq;
using System.Linq.Expressions;
using System.IO;
using System.Text;
using System.Diagnostics;

using static util;
using P = pair<int, int>;

using Binary = System.Func<System.Linq.Expressions.ParameterExpression,
                           System.Linq.Expressions.ParameterExpression,
                           System.Linq.Expressions.BinaryExpression>;
using Unary = System.Func<System.Linq.Expressions.ParameterExpression,
                          System.Linq.Expressions.UnaryExpression>;

class Program {
    static StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
    static Scan sc = new Scan();
    const int M = 1000000007;
    const int M2 = 998244353;
    const long LM = 1L << 60;
    const double eps = 1e-11;
    static void Main(string[] args)
    {
        int n, m, k;
        sc.Multi(out n, out m, out k);
        var p = sc.LongArr;
        var c = sc.IntArr.Select(x => x - 1).ToArray();
        var j = sc.LongArr;
        var edge = new List<pair<long, int>>[n];
        for (int i = 0; i < n; i++)
        {
            edge[i] = new List<pair<long, int>>();
        }
        for (int i = 0; i < m; i++)
        {
            int u, v, t;
            sc.Multi(out u, out v, out t);
            --u;
            --v;
            edge[u].Add(new pair<long, int>(t, v));
            edge[v].Add(new pair<long, int>(t, u));
        }
        var sp = new ShortestPath<long>(LM);
        var distFrom0 = sp.Dijkstra(edge, 0);

        var distP = new long[n];
        {
            var q = new PriorityQueue<pair<long, int>>();
            for (int i = 0; i < n; ++i) {
                distP[i] = p[i];
                q.Push(new pair<long, int>(distP[i], i));
            }
            while (q.Count > 0) {
                var pp = q.Pop();
                if (distP[pp.v2] > pp.v1) continue;
                foreach (var e in edge[pp.v2]) {
                    long d = pp.v1 - e.v1 * 2;
                    if (distP[e.v2] < d) {
                        distP[e.v2] = d;
                        q.Push(make_pair(d, e.v2));
                    }
                }
            }
        }
        var distL = new long[n];
        {
            var q = new PriorityQueue<pair<long, int>>();
            for (int i = 0; i < n; ++i) {
                distL[i] = p[i] - distFrom0[i];
                q.Push(new pair<long, int>(distL[i], i));
            }
            while (q.Count > 0) {
                var pp = q.Pop();
                if (distL[pp.v2] > pp.v1) continue;
                foreach (var e in edge[pp.v2]) {
                    long d = pp.v1 - e.v1;
                    if (distL[e.v2] < d) {
                        distL[e.v2] = d;
                        q.Push(make_pair(d, e.v2));
                    }
                }
            }
        }
        var ans = new long[k];
        for (int i = 0; i < k; i++)
        {
            ans[i] = -LM;
        }
        for (int i = 0; i < n; i++)
        {
            ans[c[i]] = Math.Max(ans[c[i]], Math.Max(distP[i] + j[i] - 2 * distFrom0[i], distL[i] + j[i] - distFrom0[i]));
        }
        foreach (var item in ans)
        {
            Prt(item);
        }
        sw.Flush();
    }

    static void DBG(string a) => Console.WriteLine(a);
    static void DBG<T>(IEnumerable<T> a) => DBG(string.Join(" ", a));
    static void DBG(params object[] a) => DBG(string.Join(" ", a));
    static void Prt(string a) => sw.WriteLine(a);
    static void Prt<T>(IEnumerable<T> a) => Prt(string.Join(" ", a));
    static void Prt(params object[] a) => Prt(string.Join(" ", a));
}
class pair<T, U> : IComparable<pair<T, U>> {
    public T v1;
    public U v2;
    public pair() : this(default(T), default(U)) {}
    public pair(T v1, U v2) { this.v1 = v1; this.v2 = v2; }
    public int CompareTo(pair<T, U> a) {
        int c = Comparer<T>.Default.Compare(v1, a.v1);
        return c != 0 ? c : Comparer<U>.Default.Compare(v2, a.v2);
    }
    public override string ToString() => v1 + " " + v2;
    public void Deconstruct(out T a, out U b) { a = v1; b = v2; }
    public static bool operator>(pair<T, U> a, pair<T, U> b) => a.CompareTo(b) > 0;
    public static bool operator<(pair<T, U> a, pair<T, U> b) => a.CompareTo(b) < 0;
    public static bool operator>=(pair<T, U> a, pair<T, U> b) => a.CompareTo(b) >= 0;
    public static bool operator<=(pair<T, U> a, pair<T, U> b) => a.CompareTo(b) <= 0;
}
static class util {
    public static pair<T, U> make_pair<T, U>(T v1, U v2) => new pair<T, U>(v1, v2);
    public static T sq<T>(T a) => Operator<T>.Multiply(a, a);
    public static T Max<T>(params T[] a) => a.Max();
    public static T Min<T>(params T[] a) => a.Min();
    public static bool inside(int i, int j, int h, int w) => i >= 0 && i < h && j >= 0 && j < w;
    static readonly int[] dd = { 0, 1, 0, -1 };
    static readonly string dstring = "RDLU";
    public static P[] adjacents(this P p) => adjacents(p.v1, p.v2);
    public static P[] adjacents(this P p, int h, int w) => adjacents(p.v1, p.v2, h, w);
    public static pair<P, char>[] adjacents_with_str(int i, int j)
        => Enumerable.Range(0, dd.Length).Select(k => new pair<P, char>(new P(i + dd[k], j + dd[k ^ 1]), dstring[k])).ToArray();
    public static pair<P, char>[] adjacents_with_str(int i, int j, int h, int w)
        => Enumerable.Range(0, dd.Length).Select(k => new pair<P, char>(new P(i + dd[k], j + dd[k ^ 1]), dstring[k])).Where(p => inside(p.v1.v1, p.v1.v2, h, w)).ToArray();
    public static P[] adjacents(int i, int j)
        => Enumerable.Range(0, dd.Length).Select(k => new P(i + dd[k], j + dd[k ^ 1])).ToArray();
    public static P[] adjacents(int i, int j, int h, int w)
        => Enumerable.Range(0, dd.Length).Select(k => new P(i + dd[k], j + dd[k ^ 1])).Where(p => inside(p.v1, p.v2, h, w)).ToArray();
    public static void Assert(bool cond) { if (!cond) throw new Exception(); }
    public static Dictionary<T, int> compress<T>(this IEnumerable<T> a)
        => a.Distinct().OrderBy(v => v).Select((v, i) => new { v, i }).ToDictionary(p => p.v, p => p.i);
    public static Dictionary<T, int> compress<T>(params IEnumerable<T>[] a) => compress(a.Aggregate(Enumerable.Union));
    public static void swap<T>(ref T a, ref T b) where T : struct { var t = a; a = b; b = t; }
    public static void swap<T>(this IList<T> a, int i, int j) where T : struct { var t = a[i]; a[i] = a[j]; a[j] = t; }
    public static T[] copy<T>(this IList<T> a) {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
}
static class Operator<T> {
    static readonly ParameterExpression x = Expression.Parameter(typeof(T), "x");
    static readonly ParameterExpression y = Expression.Parameter(typeof(T), "y");
    public static readonly Func<T, T, T> Add = Lambda(Expression.Add);
    public static readonly Func<T, T, T> Subtract = Lambda(Expression.Subtract);
    public static readonly Func<T, T, T> Multiply = Lambda(Expression.Multiply);
    public static readonly Func<T, T, T> Divide = Lambda(Expression.Divide);
    public static readonly Func<T, T> Plus = Lambda(Expression.UnaryPlus);
    public static readonly Func<T, T> Negate = Lambda(Expression.Negate);
    public static Func<T, T, T> Lambda(Binary op) => Expression.Lambda<Func<T, T, T>>(op(x, y), x, y).Compile();
    public static Func<T, T> Lambda(Unary op) => Expression.Lambda<Func<T, T>>(op(x), x).Compile();
}

class Scan {
    StreamReader sr;
    public Scan() { sr = new StreamReader(Console.OpenStandardInput()); }
    public Scan(string path) { sr = new StreamReader(path); }
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public string Str => sr.ReadLine().Trim();
    public pair<T, U> Pair<T, U>() {
        T a; U b;
        Multi(out a, out b);
        return new pair<T, U>(a, b);
    }
    public P P => Pair<int, int>();
    public int[] IntArr => StrArr.Select(int.Parse).ToArray();
    public long[] LongArr => StrArr.Select(long.Parse).ToArray();
    public double[] DoubleArr => StrArr.Select(double.Parse).ToArray();
    public string[] StrArr => Str.Split(new[]{' '}, StringSplitOptions.RemoveEmptyEntries);
    bool eq<T, U>() => typeof(T).Equals(typeof(U));
    T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
    T cv<T>(string s) => eq<T, int>()    ? ct<T, int>(int.Parse(s))
                       : eq<T, long>()   ? ct<T, long>(long.Parse(s))
                       : eq<T, double>() ? ct<T, double>(double.Parse(s))
                       : eq<T, char>()   ? ct<T, char>(s[0])
                                         : ct<T, string>(s);
    public void Multi<T>(out T a) => a = cv<T>(Str);
    public void Multi<T, U>(out T a, out U b)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); }
    public void Multi<T, U, V>(out T a, out U b, out V c)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); }
    public void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); }
    public void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); }
}

class ShortestPath<T> where T : struct, IComparable<T>
{
    T Inf;
    public ShortestPath(T inf) { Inf = inf; }
    T min(T a, T b) => a.CompareTo(b) > 0 ? b : a;
    T Add(T a, T b) => Operator<T>.Add(a, b);
    public T[][] WarshallFloyd(T[][] g)
    {
        var d = Copy(g);
        int n = d.Length;
        for (int i = 0; i < n; ++i) for (int j = 0; j < n; ++j) for (int k = 0; k < n; ++k) d[j][k] = min(d[j][k], Add(d[j][i], d[i][k]));
        return d;
    }
    T[][] Copy(T[][] g)
    {
        int n = g.Length;
        var ret = new T[n][];
        for (int i = 0; i < n; ++i)
        {
            ret[i] = new T[n];
            for (int j = 0; j < n; ++j)
            {
                if (i != j && g[i][j].Equals(default(T))) ret[i][j] = Inf;
                else ret[i][j] = g[i][j];
            }
        }
        return ret;
    }

    public T[] Dijkstra(List<pair<T, int>>[] edges, int s)
    {
        int n = edges.Length;
        var dist = new T[n];
        var q = new PriorityQueue<pair<T, int>>(){ rev = true };
        for (int i = 0; i < n; ++i) dist[i] = Inf;
        dist[s] = default(T);
        q.Push(make_pair(dist[s], s));
        while (q.Count > 0) {
            var p = q.Pop();
            if (dist[p.v2].CompareTo(p.v1) < 0) continue;
            foreach (var e in edges[p.v2]) {
                T d = Add(p.v1, e.v1);
                if (dist[e.v2].CompareTo(d) > 0) {
                    dist[e.v2] = d;
                    q.Push(make_pair(d, e.v2));
                }
            }
        }
        return dist;
    }
    public T[] Dijkstra(List<pair<T, int>>[] edges, int s, out long[] cnt, long Mod)
    {
        int n = edges.Length;
        var dist = new T[n];
        var q = new PriorityQueue<pair<T, int>>(){ rev = true };
        for (int i = 0; i < n; ++i) dist[i] = Inf;
        dist[s] = default(T);
        q.Push(make_pair(dist[s], s));
        cnt = new long[n];
        cnt[s] = 1;
        while (q.Count > 0) {
            var p = q.Pop();
            if (dist[p.v2].CompareTo(p.v1) < 0) continue;
            foreach (var e in edges[p.v2]) {
                T d = Add(p.v1, e.v1);
                if (dist[e.v2].CompareTo(d) > 0) {
                    dist[e.v2] = d;
                    cnt[e.v2] = cnt[p.v2];
                    q.Push(make_pair(d, e.v2));
                }
                else if (dist[e.v2].CompareTo(d) == 0) {
                    cnt[e.v2] = (cnt[e.v2] + cnt[p.v2]) % Mod;
                }
            }
        }
        return dist;
    }
}

// the greatest element pops
class PriorityQueue<T> where T : IComparable<T> {
    List<T> buf;
    public bool rev = false;
    public PriorityQueue() { buf = new List<T>(); }
    int cmp(int i, int j) => buf[i].CompareTo(buf[j]) * (rev ? -1 : 1);
    void swap(int i, int j) { var t = buf[i]; buf[i] = buf[j]; buf[j] = t; }
    public void Push(T elem) {
        int n = buf.Count;
        buf.Add(elem);
        while (n > 0) {
            int i = (n - 1) >> 1;
            if (cmp(n, i) > 0) swap(i, n);
            n = i;
        }
    }
    public T Pop() {
        T ret = buf[0];
        int n = buf.Count - 1;
        buf[0] = buf[n];
        buf.RemoveAt(n);
        for (int i = 0, j; (j = (i << 1) + 1) < n; i = j) {
            if (j != n - 1 && cmp(j, j + 1) < 0) ++j;
            if (cmp(i, j) < 0) swap(i, j);
        }
        return ret;
    }
    public T Top => buf[0];
    public int Count => buf.Count;
}

class PriorityQueue_rev_int {
    List<int> buf;
    public PriorityQueue_rev_int() { buf = new List<int>(); }
    // int cmp(int i, int j) => buf[i].CompareTo(buf[j]) * (rev ? -1 : 1);
    void swap(int i, int j) { var t = buf[i]; buf[i] = buf[j]; buf[j] = t; }
    public void Push(int elem) {
        int n = buf.Count;
        buf.Add(elem);
        while (n > 0) {
            int i = (n - 1) >> 1;
            if (buf[n] < buf[i]) swap(i, n);
            n = i;
        }
    }
    public int Pop() {
        int ret = buf[0];
        int n = buf.Count - 1;
        buf[0] = buf[n];
        buf.RemoveAt(n);
        for (int i = 0, j; (j = (i << 1) + 1) < n; i = j) {
            if (j != n - 1 && buf[j] > buf[j + 1]) ++j;
            if (buf[i] > buf[j]) swap(i, j);
        }
        return ret;
    }
    public int Top => buf[0];
    public int Count => buf.Count;
}



Measured memory_bytes: 71412