Problem: Whoso in ignorance draws near to them and hears the Sirens' voice, he nevermore returns.

Homer, Odyssey

In the times of Jason and the Argonauts, it was well known that sirens use the sound of their songs to lure sailors into their demise. Yet only a few knew that every time sirens call a sailor by his name, his will weakens, making him more vulnerable. 

For the purpose of this problem, both siren songs and names of the sailors will be represented as strings of lowercase English letters. The more times the sailor's name occurs as a contiguous substring of the song, the greater danger he is in.

Jason found out that sirens can sing one of the n+1 songs, which have the following structure: let s_i (0 ≤ i ≤ n) be the i-th song and t be a string of length n, then for every i < n: s_{i+1} = s_i t_i s_i. In other words i+1-st song is the concatenation of i-th song, i-th letter (0-indexed) of t and the i-th song. 

Fortunately, he also knows s_0 and t. Jason wonders how many times a sailor's name is mentioned in a particular song. Answer q queries: given the sailor's name (w) and the index of a song (i) output the number of occurrences of w in s_i as a substring. As this number can be quite large, output its remainder modulo 10^9+7.

Input

In the first line of input there are two integers n, q (  1 ≤ n, q ≤ 10^5) meaning that there are n+1 songs and q queries. In the next two lines strings s_0 and t follow (1 ≤ |s_0| ≤ 100, |t| = n). 

Next q lines describe the queries; each one contains an integer k ( 0 ≤ k ≤ n), the index of the song sung by the sirens, and a non-empty string w, which is the name of a sailor. All strings in this problem consist only of lowercase English letters, and the sum of lengths of sailors' names does not exceed 10^6.

Output

Output q lines, i-th of them should contain the remainder modulo 10^9+7 of the number of occurrences of w in s_k.

Examples

Input


3 3
aa
bcd
2 aba
3 ca
3 aa


Output


2
2
8


Input


4 5
aba
bbac
1 a
3 baca
3 ab
2 bab
4 aba


Output


4
0
14
6
28

Note

In the first example songs of the sirens are as follows: 

  * Song 0: aa
  * Song 1: aabaa
  * Song 2: aabaacaabaa
  * Song 3: aabaacaabaadaabaacaabaa

Solution (in JAVA):

Solution:
//package goodbye2020;
import java.io.*;
import java.util.*;

public class G {
	InputStream is;
	FastWriter out;
	String INPUT = "";

	final int mod = 1000000007;
	long ans = 0;
	long[] p2 = enumPows(2, 1000305, mod);
	long[][] dp;
	char[] t;

	void solve()
	{
		Random gen = new Random();
		int M = gen.nextInt(10000)*2+3;

		int n = ni(), Q = ni();
		char[] s0 = ns().toCharArray();
		int m = s0.length;
		t = ns(n);

		RollingHash61 rh = new RollingHash61(M, m);
		for(char c : s0){
			rh.add(c);
		}
		Map<Long, Integer> s0hit = new HashMap<>();
		for(int i = 0;i < m;i++){
			for(int j = i+1;j <= m;j++){
				s0hit.merge(rh.h(i, j), 1, Integer::sum);
			}
		}
		long rhh = rh.h(0, m);

		dp = new long[26][n+1];
		for(int i = 0;i < 26;i++){
			for(int j = 1;j <= n;j++){
				dp[i][j] = dp[i][j-1] * 2 + (t[j-1]-'a' == i ? 1 : 0);
				dp[i][j] %= mod;
			}
		}

		for(int z = 0;z < Q;z++){
			ans = 0;
			int K = ni();
			char[] q = ns().toCharArray();
			RollingHash61 lrh = new RollingHash61(M, q.length);
			for(char c : q)lrh.add(c);

			if(q.length <= s0.length){
				ans += s0hit.getOrDefault(lrh.h(0, q.length), 0) * p2[K];
				ans %= mod;
			}

			// s0's offset
			boolean[] same = new boolean[m+1];
			Arrays.fill(same, true);
			for(int i = 0, j = 0;i < q.length;i++,j++){
				if(j == m+1)j = 0;
				if(q[i] != q[j])same[j] = false;
			}
			int nsame = 0;
			int el = -1;
			for(int i = 0;i < m+1;i++){
				if(same[i]){
					nsame++;
				}else{
					el = i;
				}
			}
			if(nsame >= m){
				RollingHash61 lrh2 = null;
				if(q.length >= m+1) {
					lrh2 = new RollingHash61(M, (m+1)*2);
					for (int i = 0;i < m+1;i++)lrh2.add(q[i]);
					for (int i = 0;i < m+1;i++)lrh2.add(q[i]);
				}

				for(int offset = 0;offset < m+1 && offset < q.length;offset++){
					if(el != -1 && offset != el)continue;
					if(q.length >= m+1) {
						if (lrh2.h(offset + 1, offset + 1 + m) == rhh) {
							dfs(offset, m+1, 1, K, q);
						}
					}else{
						if(lrh.h(0, offset) == rh.h(m-offset, m) &&
							lrh.h(offset+1, q.length) == rh.h(0, q.length-(offset+1))){
							ans += dp[q[offset]-'a'][K];
						}
					}
				}
			}
			ans %= mod;
			if(ans < 0)ans += mod;
			out.println(ans);
		}
	}

	void dfs(int base, int w, int phase, int phaselim, char[] q)
	{
//		for(int u = 0;u < 21 && base+w < q.length;u++){
		if(phaselim-phase+1 < 1)return;

		if(base + w >= q.length){
			// 2^(phaselim-phase)+...+1
			ans += dp[q[base]-'a'][phaselim] - dp[q[base]-'a'][phase-1] * p2[phaselim - phase+1];
			ans %= mod;
			return;
		}

		inner:
		for(int bb = base;bb <= base+w;bb += w) {
			for (int x = bb; x < q.length; x += 2 * w) {
				if (q[x] != t[phase-1])continue inner;
			}
			dfs(base ^ base + w ^ bb, 2*w, phase+1, phaselim, q);
		}
	}

	public static long[] enumPows(int a, int n, int mod)
	{
		a %= mod;
		long[] pows = new long[n+1];
		pows[0] = 1;
		for(int i = 1;i <= n;i++)pows[i] = pows[i-1] * a % mod;
		return pows;
	}



	public static class RollingHash61
	{
		static final long mod = (1L<<61)-1;
		public long M;
		public long[] pows;
		public long[] hs;
		public int hp;

		public RollingHash61(long M, int n) {
			assert M > 0;
			assert n > 0;
			this.M = M;
			this.pows = makePows(M, n);
			this.hs = new long[n+1];
			this.hp = 0;
		}

		public static long mul(long a, long b)
		{
			long al = a&(1L<<31)-1, ah = a>>>31;
			long bl = b&(1L<<31)-1, bh = b>>>31;
			long low = al * bl; // <2^62
			long mid = al * bh + bl * ah; // < 2^62
			long high = ah * bh + (mid>>>31); // < 2^60 + 2^31 < 2^61
			// high*2^62 = high*2 (mod 2^61-1)
			long ret = mod(mod(2*high + low) + ((mid&(1L<<31)-1)<<31));
			return ret;
		}

		public static long mod(long a)
		{
			while(a >= mod)a -= mod;
			while(a < 0)a += mod;
			return a;
		}

		private static long[] makePows(long M, int n)
		{
			long[] ret = new long[n+1];
			ret[0] = 1;
			for(int i = 1;i <= n;i++)ret[i] = mul(ret[i-1], M);
			return ret;
		}

		public void add(long x)
		{
			hs[hp+1] = mul(hs[hp], M) + x;
			if(hs[hp+1] >= mod)hs[hp+1] -= mod;
			hp++;
		}

		public long h(int l, int r)
		{
			assert l <= r;
			return mod(hs[r] - mul(hs[l], pows[r-l]));
		}
	}


	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new FastWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new G().run(); }
	
	private byte[] inbuf = new byte[1024];
	public 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 int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}

	private long[] nal(int n)
	{
		long[] a = new long[n];
		for(int i = 0;i < n;i++)a[i] = nl();
		return a;
	}

	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[][] nmi(int n, int m) {
		int[][] map = new int[n][];
		for(int i = 0;i < n;i++)map[i] = na(m);
		return map;
	}

	private int ni() { return (int)nl(); }

	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();
		}
	}

	public static class FastWriter
	{
		private static final int BUF_SIZE = 1<<13;
		private final byte[] buf = new byte[BUF_SIZE];
		private final OutputStream out;
		private int ptr = 0;

		private FastWriter(){out = null;}

		public FastWriter(OutputStream os)
		{
			this.out = os;
		}

		public FastWriter(String path)
		{
			try {
				this.out = new FileOutputStream(path);
			} catch (FileNotFoundException e) {
				throw new RuntimeException("FastWriter");
			}
		}

		public FastWriter write(byte b)
		{
			buf[ptr++] = b;
			if(ptr == BUF_SIZE)innerflush();
			return this;
		}

		public FastWriter write(char c)
		{
			return write((byte)c);
		}

		public FastWriter write(char[] s)
		{
			for(char c : s){
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			}
			return this;
		}

		public FastWriter write(String s)
		{
			s.chars().forEach(c -> {
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			});
			return this;
		}

		private static int countDigits(int l) {
			if (l >= 1000000000) return 10;
			if (l >= 100000000) return 9;
			if (l >= 10000000) return 8;
			if (l >= 1000000) return 7;
			if (l >= 100000) return 6;
			if (l >= 10000) return 5;
			if (l >= 1000) return 4;
			if (l >= 100) return 3;
			if (l >= 10) return 2;
			return 1;
		}

		public FastWriter write(int x)
		{
			if(x == Integer.MIN_VALUE){
				return write((long)x);
			}
			if(ptr + 12 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		private static int countDigits(long l) {
			if (l >= 1000000000000000000L) return 19;
			if (l >= 100000000000000000L) return 18;
			if (l >= 10000000000000000L) return 17;
			if (l >= 1000000000000000L) return 16;
			if (l >= 100000000000000L) return 15;
			if (l >= 10000000000000L) return 14;
			if (l >= 1000000000000L) return 13;
			if (l >= 100000000000L) return 12;
			if (l >= 10000000000L) return 11;
			if (l >= 1000000000L) return 10;
			if (l >= 100000000L) return 9;
			if (l >= 10000000L) return 8;
			if (l >= 1000000L) return 7;
			if (l >= 100000L) return 6;
			if (l >= 10000L) return 5;
			if (l >= 1000L) return 4;
			if (l >= 100L) return 3;
			if (l >= 10L) return 2;
			return 1;
		}

		public FastWriter write(long x)
		{
			if(x == Long.MIN_VALUE){
				return write("" + x);
			}
			if(ptr + 21 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		public FastWriter write(double x, int precision)
		{
			if(x < 0){
				write('-');
				x = -x;
			}
			x += Math.pow(10, -precision)/2;
			//		if(x < 0){ x = 0; }
			write((long)x).write(".");
			x -= (long)x;
			for(int i = 0;i < precision;i++){
				x *= 10;
				write((char)('0'+(int)x));
				x -= (int)x;
			}
			return this;
		}

		public FastWriter writeln(char c){
			return write(c).writeln();
		}

		public FastWriter writeln(int x){
			return write(x).writeln();
		}

		public FastWriter writeln(long x){
			return write(x).writeln();
		}

		public FastWriter writeln(double x, int precision){
			return write(x, precision).writeln();
		}

		public FastWriter write(int... xs)
		{
			boolean first = true;
			for(int x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter write(long... xs)
		{
			boolean first = true;
			for(long x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter writeln()
		{
			return write((byte)'\n');
		}

		public FastWriter writeln(int... xs)
		{
			return write(xs).writeln();
		}

		public FastWriter writeln(long... xs)
		{
			return write(xs).writeln();
		}

		public FastWriter writeln(char[] line)
		{
			return write(line).writeln();
		}

		public FastWriter writeln(char[]... map)
		{
			for(char[] line : map)write(line).writeln();
			return this;
		}

		public FastWriter writeln(String s)
		{
			return write(s).writeln();
		}

		private void innerflush()
		{
			try {
				out.write(buf, 0, ptr);
				ptr = 0;
			} catch (IOException e) {
				throw new RuntimeException("innerflush");
			}
		}

		public void flush()
		{
			innerflush();
			try {
				out.flush();
			} catch (IOException e) {
				throw new RuntimeException("flush");
			}
		}

		public FastWriter print(byte b) { return write(b); }
		public FastWriter print(char c) { return write(c); }
		public FastWriter print(char[] s) { return write(s); }
		public FastWriter print(String s) { return write(s); }
		public FastWriter print(int x) { return write(x); }
		public FastWriter print(long x) { return write(x); }
		public FastWriter print(double x, int precision) { return write(x, precision); }
		public FastWriter println(char c){ return writeln(c); }
		public FastWriter println(int x){ return writeln(x); }
		public FastWriter println(long x){ return writeln(x); }
		public FastWriter println(double x, int precision){ return writeln(x, precision); }
		public FastWriter print(int... xs) { return write(xs); }
		public FastWriter print(long... xs) { return write(xs); }
		public FastWriter println(int... xs) { return writeln(xs); }
		public FastWriter println(long... xs) { return writeln(xs); }
		public FastWriter println(char[] line) { return writeln(line); }
		public FastWriter println(char[]... map) { return writeln(map); }
		public FastWriter println(String s) { return writeln(s); }
		public FastWriter println() { return writeln(); }
	}

	public void trnz(int... o)
	{
		for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");
		System.out.println();
	}

	// print ids which are 1
	public void trt(long... o)
	{
		Queue<Integer> stands = new ArrayDeque<>();
		for(int i = 0;i < o.length;i++){
			for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));
		}
		System.out.println(stands);
	}

	public void tf(boolean... r)
	{
		for(boolean x : r)System.out.print(x?'#':'.');
		System.out.println();
	}

	public void tf(boolean[]... b)
	{
		for(boolean[] r : b) {
			for(boolean x : r)System.out.print(x?'#':'.');
			System.out.println();
		}
		System.out.println();
	}

	public void tf(long[]... b)
	{
		if(INPUT.length() != 0) {
			for (long[] r : b) {
				for (long x : r) {
					for (int i = 0; i < 64; i++) {
						System.out.print(x << ~i < 0 ? '#' : '.');
					}
				}
				System.out.println();
			}
			System.out.println();
		}
	}

	public void tf(long... b)
	{
		if(INPUT.length() != 0) {
			for (long x : b) {
				for (int i = 0; i < 64; i++) {
					System.out.print(x << ~i < 0 ? '#' : '.');
				}
			}
			System.out.println();
		}
	}

	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}