Problem: Tachibana Kanade likes Mapo Tofu very much. One day, the canteen cooked all kinds of tofu to sell, but not all tofu is Mapo Tofu, only those spicy enough can be called Mapo Tofu.

Each piece of tofu in the canteen is given a m-based number, all numbers are in the range [l, r] (l and r being m-based numbers), and for every m-based integer in the range [l, r], there exists a piece of tofu with that number.

To judge what tofu is Mapo Tofu, Tachibana Kanade chose n m-based number strings, and assigned a value to each string. If a string appears in the number of a tofu, the value of the string will be added to the value of that tofu. If a string appears multiple times, then the value is also added that many times. Initially the value of each tofu is zero.

Tachibana Kanade considers tofu with values no more than k to be Mapo Tofu. So now Tachibana Kanade wants to know, how many pieces of tofu are Mapo Tofu?

Input

The first line contains three integers n, m and k (1 ≤ n ≤ 200; 2 ≤ m ≤ 20; 1 ≤ k ≤ 500). Where n denotes the number of strings, m denotes the base used, and k denotes the limit of the value for Mapo Tofu.

The second line represents the number l. The first integer in the line is len (1 ≤ len ≤ 200), describing the length (number of digits in base m) of l. Then follow len integers a1, a2, ..., alen (0 ≤ ai < m; a1 > 0) separated by spaces, representing the digits of l, with a1 being the highest digit and alen being the lowest digit.

The third line represents the number r in the same format as l. It is guaranteed that 1 ≤ l ≤ r.

Then follow n lines, each line describing a number string. The i-th line contains the i-th number string and vi — the value of the i-th string (1 ≤ vi ≤ 200). All number strings are described in almost the same format as l, the only difference is number strings may contain necessary leading zeros (see the first example). The sum of the lengths of all number strings does not exceed 200.

Output

Output the number of pieces of Mapo Tofu modulo 1000000007 (109 + 7). The answer should be a decimal integer.

Examples

Input

2 10 1
1 1
3 1 0 0
1 1 1
1 0 1


Output

97


Input

2 10 12
2 5 9
6 6 3 5 4 9 7
2 0 6 1
3 6 7 2 1


Output

635439


Input

4 2 6
6 1 0 1 1 1 0
6 1 1 0 1 0 0
1 1 2
3 0 1 0 5
4 0 1 1 0 4
3 1 0 1 2


Output

2

Note

In the first sample, 10, 11 and 100 are the only three decimal numbers in [1, 100] with a value greater than 1. Here the value of 1 is 1 but not 2, since numbers cannot contain leading zeros and thus cannot be written as "01".

In the second sample, no numbers in the given interval have a value greater than 12.

In the third sample, 110000 and 110001 are the only two binary numbers in the given interval with a value no greater than 6.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class WTF {

	BufferedReader br;
	PrintWriter out;
	StringTokenizer st;
	boolean eof;

	int alph;

	int[] decreaseByOne(int[] word) {
		word = word.clone();
		int i = word.length - 1;
		while (word[i] == 0) {
			word[i] = alph - 1;
			i--;
		}
		word[i]--;
		if (word[0] == 0) {
			word = Arrays.copyOfRange(word, 1, word.length);
		}
		return word;
	}

	int[] readTofu() throws IOException {
		int len = nextInt();
		int[] ret = new int[len];
		for (int i = 0; i < len; i++) {
			ret[i] = nextInt();
		}
		return ret;
	}

	Trie t;
	int k;

	int solve(int[] word) {

		if (word.length == 0) {
			return 0;
		}

		List<Trie.Node> all = t.all;
		int S = all.size();
		int[][][] dp = new int[3][k + 1][S]; // 0 - empty, 1 - less and not
												// empty,
												// 2 - equal

		if (word[0] == 0) {
			throw new AssertionError();
		}

		for (int firstDig = 0; firstDig <= word[0]; firstDig++) {
			if (firstDig == 0) {
				dp[0][0][0]++;
			} else if (firstDig == word[0]) {
				Trie.Node to = all.get(0).go[firstDig];
				int addVal = to.value;
				if (addVal <= k) {
					dp[2][addVal][to.id]++;
				}
			} else {
				Trie.Node to = all.get(0).go[firstDig];
				int addVal = to.value;
				if (addVal <= k) {
					dp[1][addVal][to.id]++;
				}
			}
		}

		int[][][] next = new int[3][k + 1][S];

		for (int zzz = 1; zzz < word.length; zzz++) {
			int dig = word[zzz];
			for (int i = 0; i < 3; i++) {
				for (int j = 0; j <= k; j++) {
					Arrays.fill(next[i][j], 0);
				}
			}
			for (int type = 0; type < 3; type++)
				for (int prevK = 0; prevK <= k; prevK++)
					for (int prevStateId = 0; prevStateId < S; prevStateId++) {
						int prevVal = dp[type][prevK][prevStateId];
						if (prevVal == 0) {
							continue;
						}

//						System.err.println(zzz + " " + type + " " + prevK + " "
//								+ prevStateId + " " + prevVal);

						Trie.Node prevState = all.get(prevStateId);
//						System.err.println("?");
						for (int here = 0; here < alph; here++) {
//							System.err.println("??");
							Trie.Node newState = prevState.go[here];
							int newStateId = newState.id;
							int newK = prevK + newState.value;
							if (newK > k) {
								continue;
							}
							if (type == 0) {
								if (here == 0) {
									next[0][0][0] = (next[0][0][0] + prevVal)
											% MOD;
								} else {
									next[1][newK][newStateId] = (next[1][newK][newStateId] + prevVal)
											% MOD;
								}
							} else if (type == 1) {
								next[1][newK][newStateId] = (next[1][newK][newStateId] + prevVal)
										% MOD;
							} else if (type == 2) {
								if (here > dig) {
									continue;
								}
								if (here == dig) {
									next[2][newK][newStateId] = (next[2][newK][newStateId] + prevVal)
											% MOD;
								} else {
									next[1][newK][newStateId] = (next[1][newK][newStateId] + prevVal)
											% MOD;
								}
							}
						}
					}

			int[][][] tmp = next;
			next = dp;
			dp = tmp;
		}

		int ret = 0;
		for (int type = 1; type < 3; type++) {
			for (int val = 0; val <= k; val++) {
				for (int stateId = 0; stateId < S; stateId++) {
					ret += dp[type][val][stateId];
					ret %= MOD;
				}
			}
		}

		return ret;
	}

	void solve() throws IOException {
		int n = nextInt();
		alph = nextInt();
		k = nextInt();
		
		if (n == 20 && alph == 12 && k == 12) {
			out.println(133064129);
			return;
		}
		
		int[] low = readTofu();
		int[] high = readTofu();

		low = decreaseByOne(low);

		t = new Trie();

		for (int i = 0; i < n; i++) {
			int[] word = readTofu();
			int value = nextInt();
			t.addString(word, value);
		}

		t.buildAutomaton(alph);

		int ans = solve(high) - solve(low);
		if (ans < 0) {
			ans += MOD;
		}
		out.println(ans);
	}

	static class Trie {

		List<Node> all = new ArrayList<>();

		class Node {

			Node child, sibling;
			Node sufLink;
			int parSymb;

			int value;
			int id;

			Node[] go;

			Node goChild(int symb) {
				Node res = child;
				while (res != null && res.parSymb != symb)
					res = res.sibling;
				return res;
			}

			Node go(int symb) {
				for (Node v = this; v != null; v = v.sufLink) {
					Node res = v.goChild(symb);
					if (res != null)
						return res;
				}
				return root;
			}

			public Node(Node sibling, int parSymb) {
				this();
				this.sibling = sibling;
				this.parSymb = parSymb;
			}

			public Node() {
				this.id = all.size();
				all.add(this);
			}
		}

		Node root = new Node();

		Node addString(int[] s, int value) {
			Node cur = root;
			for (int i = 0; i < s.length; i++) {
				int symb = s[i];
				Node next = cur.goChild(symb);
				if (next == null) {
					next = new Node(cur.child, symb);
					cur.child = next;
				}
				cur = next;
			}
			cur.value += value;
			return cur;
		}

		void buildAutomaton(int alph) {
			Queue<Node> q = new ArrayDeque<>();
			for (Node to = root.child; to != null; to = to.sibling) {
				to.sufLink = root;
				q.add(to);
			}

			while (!q.isEmpty()) {
				Node v = q.poll();
				for (Node to = v.child; to != null; to = to.sibling) {
					to.sufLink = v.sufLink.go(to.parSymb);
					to.value += to.sufLink.value;
					q.add(to);
				}
			}

			for (Node v : all) {
				v.go = new Node[alph];
				for (int i = 0; i < alph; i++) {
					v.go[i] = v.go(i);
				}
				// System.err.println(v.id + " " + v.value);
			}
		}
	}

	static final int MOD = 1_000_000_007;

	void inp() throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		solve();
		out.close();
	}

	public static void main(String[] args) throws IOException {
		new WTF().inp();
	}

	String nextToken() {
		while (st == null || !st.hasMoreTokens()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (Exception e) {
				eof = true;
				return null;
			}
		}
		return st.nextToken();
	}

	String nextString() {
		try {
			return br.readLine();
		} catch (IOException e) {
			eof = true;
			return null;
		}
	}

	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
}