Problem: Barney was hanging out with Nora for a while and now he thinks he may have feelings for her. Barney wants to send her a cheesy text message and wants to make her as happy as possible.

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Initially, happiness level of Nora is 0. Nora loves some pickup lines like "I'm falling for you" and stuff. Totally, she knows n pickup lines, each consisting only of lowercase English letters, also some of them may be equal (in writing, but different in pronouncing or meaning though). Every time Nora sees i-th pickup line as a consecutive subsequence of Barney's text message her happiness level increases by ai. These substrings may overlap, for example, Nora will see the pickup line aa twice and the pickup line ab once in text message aaab.

Due to texting app limits, Barney's text may have up to l characters.

Barney asked you to help him make Nora as much happy as possible, it's gonna be legen...

Input

The first line of input contains two integers n and l (1 ≤ n ≤ 200, 1 ≤ l ≤ 1014) — the number of pickup lines and the maximum length of Barney's text.

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 100), meaning that Nora's happiness level increases by ai after every time seeing i-th pickup line.

The next n lines contain the pickup lines. i-th of them contains a single string si consisting of only English lowercase letter. Summary length of all pickup lines does not exceed 200.

All strings are not empty.

Output

Print the only integer — the maximum possible value of Nora's happiness level after reading Barney's text.

Examples

Input

3 6
3 2 1
heart
earth
art


Output

6


Input

3 6
3 2 8
heart
earth
art


Output

16

Note

An optimal answer for the first sample case is hearth containing each pickup line exactly once.

An optimal answer for the second sample case is artart.

Solution (in JAVA):

Solution:
//package round362;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Queue;

public class D {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni();
		long L = nl();
		int[] a = na(n);
		TrieByLink trie = new TrieByLink();
		for(int i = 0;i < n;i++){
			trie.add(ns().toCharArray(), a[i]);
		}
		trie.buildFailure();
		long[][] M = new long[trie.gen][trie.gen];
		for(int i = 0;i < trie.gen;i++){
			Arrays.fill(M[i], -1);
		}
		for(TrieByLink.Node node : trie.toArray()){
			int ved = 0;
			for(TrieByLink.Node f = node;f != null;f = f.fail){
				for(TrieByLink.Node ch = f.firstChild;ch != null;ch = ch.next){
					if(ved<<~(ch.c-'a')>=0){
						ved |= 1<<ch.c-'a';
						M[ch.id][node.id] = ch.hit;
					}
				}
			}
		}
		long[] v = new long[trie.gen];
		Arrays.fill(v, -1);
		v[0] = 0;
//		for(int x = 1;x < 10;x++){
//			tr(x, pow(M, v, x));
//		}
		out.println(Arrays.stream(pow(M, v, L)).max().getAsLong());
	}
	
	public static long[] mul(long[][] A, long[] v)
	{
		int m = A.length;
		int n = v.length;
		long[] w = new long[m];
		for(int i = 0;i < m;i++){
			long sum = -1;//Long.MIN_VALUE;
			for(int k = 0;k < n;k++){
				if(A[i][k] < 0 || v[k] < 0)continue;
				long x = A[i][k] + v[k];
				if(x > sum)sum = x;
			}
			w[i] = sum;
		}
		return w;
	}
	
	public static long[][] p2(long[][] A)
	{
		int n = A.length;
		long[][] C = new long[n][n];
		for(int i = 0;i < n;i++){
			Arrays.fill(C[i], Long.MIN_VALUE);
			for(int k = 0;k < n;k++){
				for(int j = 0;j < n;j++){
					long x = A[i][k] < 0 || A[k][j] < 0 ? -1 : A[i][k] + A[k][j];
					if(x > C[i][j])C[i][j] = x;
				}
			}
		}
		return C;
	}
	
	// A^e*v
	public static long[] pow(long[][] A, long[] v, long m)
	{
		long[][] mu = A;
		long[] r = v;
		for(;m > 0;m>>>=1){
			if(m<<63<0)r = mul(mu, r);
			mu = p2(mu);
		}
		return r;
	}
	
	public static class TrieByLink {
		public Node root = new Node((char)0, 0);
		public int gen = 1;
		public static final char[] atoz = "abcdefghijklmnopqrstuvwxyz".toCharArray();
		
		public static class Node
		{
			public int id;
			public char c;
			public Node next, firstChild;
			public int hit = 0;
			
			public Node fail;
			
			public Node(char c, int id)
			{
				this.id = id;
				this.c = c;
			}
			
			public String toString(String indent)
			{
				StringBuilder sb = new StringBuilder();
				sb.append(indent + id + ":" + c);
				if(hit != 0)sb.append(" H:" + hit);
				if(fail != null)sb.append(" F:" + fail.id);
				sb.append("\n");
				for(Node c = firstChild;c != null; c = c.next){
					sb.append(c.toString(indent + "  "));
				}
				return sb.toString();
			}
		}
		
		public void add(char[] s, int score)
		{
			Node cur = root;
			Node pre = null;
			for(char c : s){
				pre = cur; cur = cur.firstChild;
				if(cur == null){
					cur = pre.firstChild = new Node(c, gen++);
				}else{
					for(;cur != null && cur.c != c;pre = cur, cur = cur.next);
					if(cur == null)cur = pre.next = new Node(c, gen++);
				}
			}
			cur.hit += score;
		}
		
		public void buildFailure()
		{
			root.fail = null;
			Queue<Node> q = new ArrayDeque<Node>();
			q.add(root);
			while(!q.isEmpty()){
				Node cur = q.poll();
				inner:
				for(Node ch = cur.firstChild;ch != null; ch = ch.next){
					q.add(ch);
					for(Node to = cur.fail; to != null; to = to.fail){
						for(Node lch = to.firstChild;lch != null; lch = lch.next){
							if(lch.c == ch.c){
								ch.fail = lch;
								ch.hit += lch.hit; // propagation of hit
								continue inner;
							}
						}
					}
					ch.fail = root;
				}
			}
		}
		
		public Node next(Node cur, char c)
		{
			for(;cur != null;cur = cur.fail){
				for(Node ch = cur.firstChild;ch != null; ch = ch.next){
					if(ch.c == c)return ch;
				}
			}
			return root;
		}
		
		public int[][] ngMatrix(char[] cs)
		{
			int[] map = new int[128];
			Arrays.fill(map, -1);
			for(int i = 0;i < cs.length;i++)map[cs[i]] = i;
			
			int[][] a = new int[gen+1][gen+1];
			Node[] nodes = toArray();
			for(int i = 0;i < gen;i++){
				if(nodes[i].hit > 0)continue;
				int nohit = cs.length;
				boolean[] ved = new boolean[cs.length];
				for(Node cur = nodes[i];cur != null;cur = cur.fail){
					for(Node ch = cur.firstChild;ch != null; ch = ch.next){
						if(map[ch.c] >= 0 && !ved[map[ch.c]]){
							ved[map[ch.c]] = true;
							if(ch.hit == 0)a[ch.id][i]++;
							nohit--;
						}
					}
				}
				a[0][i] += nohit;
			}
			Arrays.fill(a[gen], 1);
			return a;
		}
		
		public int[][] okMatrix(char[] cs)
		{
			int[] map = new int[128];
			Arrays.fill(map, -1);
			for(int i = 0;i < cs.length;i++)map[cs[i]] = i;
			
			int[][] a = new int[gen+1][gen+1];
			Node[] nodes = toArray();
			for(int i = 0;i < gen;i++){
				if(nodes[i].hit > 0)continue;
				int nohit = cs.length;
				boolean[] ved = new boolean[cs.length];
				for(Node cur = nodes[i];cur != null;cur = cur.fail){
					for(Node ch = cur.firstChild;ch != null; ch = ch.next){
						if(map[ch.c] >= 0 && !ved[map[ch.c]]){
							ved[map[ch.c]] = true;
							if(ch.hit > 0){
								a[gen][i]++;
							}else{
								a[ch.id][i]++;
							}
							nohit--;
						}
					}
				}
				a[0][i] += nohit;
			}
			a[gen][gen]++;
			return a;
		}
		
		public void search(char[] q)
		{
			Node cur = root;
			outer:
			for(char c : q){
				for(;cur != null;cur = cur.fail){
					for(Node ch = cur.firstChild;ch != null; ch = ch.next){
						if(ch.c == c){
							// ch.hit
							cur = ch;
							continue outer;
						}
					}
				}
				cur = root;
			}
		}
		
		public int countHit(char[] q)
		{
			Node cur = root;
			int hit = 0;
			outer:
			for(char c : q){
				for(;cur != null;cur = cur.fail){
					for(Node ch = cur.firstChild;ch != null; ch = ch.next){
						if(ch.c == c){
							hit += ch.hit; // add hit
							cur = ch;
							continue outer;
						}
					}
				}
				cur = root;
			}
			return hit;
		}
		
		public Node[] toArray()
		{
			Node[] ret = new Node[gen];
			ret[0] = root;
			for(int i = 0;i < gen;i++){
				Node cur = ret[i];
				if(cur.next != null)ret[cur.next.id] = cur.next;
				if(cur.firstChild != null)ret[cur.firstChild.id] = cur.firstChild;
			}
			return ret;
		}
		
		public String toString()
		{
			return root.toString("");
		}
	}

	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new D().run(); }
	
	private byte[] inbuf = new byte[1024];
	private int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}