Problem: The famous sculptor Cicasso is a Reberlandian spy!

These is breaking news in Berlandian papers today. And now the sculptor is hiding. This time you give the shelter to the maestro. You have a protected bunker and you provide it to your friend. You set the security system in such way that only you can open the bunker. To open it one should solve the problem which is hard for others but is simple for you.

Every day the bunker generates a codeword s. Every time someone wants to enter the bunker, integer n appears on the screen. As the answer one should enter another integer — the residue modulo 109 + 7 of the number of strings of length n that consist only of lowercase English letters and contain the string s as the subsequence.

The subsequence of string a is a string b that can be derived from the string a by removing some symbols from it (maybe none or all of them). In particular any string is the subsequence of itself. For example, the string "cfo" is the subsequence of the string "codeforces".

You haven't implemented the algorithm that calculates the correct answers yet and you should do that ASAP.

Input

The first line contains integer m (1 ≤ m ≤ 105) — the number of the events in the test case.

The second line contains nonempty string s — the string generated by the bunker for the current day.

The next m lines contain the description of the events. The description starts from integer t — the type of the event.

If t = 1 consider a new day has come and now a new string s is used. In that case the same line contains a new value of the string s.

If t = 2 integer n is given (1 ≤ n ≤ 105). This event means that it's needed to find the answer for the current string s and the value n.

The sum of lengths of all generated strings doesn't exceed 105. All of the given strings consist only of lowercase English letters.

Output

For each query of the type 2 print the answer modulo 109 + 7 on the separate line.

Example

Input

3
a
2 2
1 bc
2 5


Output

51
162626

Note

In the first event words of the form "a?" and "?a" are counted, where ? is an arbitrary symbol. There are 26 words of each of these types, but the word "aa" satisfies both patterns, so the answer is 51.

Solution (in JAVA):

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

public class C666 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int Z = 100005;
		int mod = 1000000007;
		
//		long[][] dp = new long[15][15];
//		dp[0][0] = 1;
//		for(int i = 1;i < 15;i++){
//			for(int j = 0;j <= i;j++){
//				dp[i][j] += dp[i-1][j] * 25;
//				if(j-1 >= 0)dp[i][j] += dp[i-1][j-1];
//			}
//			for(int j = 0;j <= i;j++)dp[i][j] %= mod;
////			tr(dp[i]);
//		}
		
		int[][] fif = enumFIF(Z, mod);
		int Q = ni();
		int n = ns().length()-1;
		int S = (int)Math.sqrt(Z);
		long[][] cs = new long[Z/S+1][];
		long[] px = new long[Z+1];
		px[0] = 1;
		for(int i = 1;i <= Z;i++){
			px[i] = px[i-1] * 25 % mod;
		}
		long[] py = new long[Z+1];
		py[0] = 1;
		for(int i = 1;i <= Z;i++){
			py[i] = py[i-1] * 26 % mod;
		}
		for(int i = 0, j = 0;i < Z/S+1 && j < Z;i++,j+=S){
			cs[i] = new long[j+1];
			for(int k = 0;k <= j;k++){
				cs[i][k] = px[j-k] * C(j, k, mod, fif) % mod;
			}
			for(int k = 1;k <= j;k++){
				cs[i][k] += cs[i][k-1];
				if(cs[i][k] >= mod)cs[i][k] -= mod;
			}
		}
		
		
		long[][] f = new long[S][S+5];
		Arrays.fill(f[0], 1);
		for(int i = 1;i < S;i++){
			for(int j = 0;j < S+5;j++){
				if(j-1 >= 0)f[i][j] += f[i-1][j-1] * 1;
				f[i][j] += f[i-1][j] * 25;
			}
			for(int j = 0;j < S+5;j++){
				f[i][j] %= mod;
			}
//			tr(f[i]);
		}
		
		for(int z = 0;z < Q;z++){
			int t = ni();
			if(t == 1){
				n = ns().length()-1;
			}else{
				int x = ni();
				if(x < n){
					out.println(0);
					continue;
				}
//				tr("go", x, n);
				// (x,n)
				int u = x/S;
				long base = n-(x-u*S) >= 0 ? cs[u][n-(x-u*S)] * py[x-u*S] % mod : 0;
//				tr("base", base);
//				tr(f[x-u*S]);
				for(int i = 0;i < x-u*S;i++){
					// (u*S,n-i) = (u*S
					if(n-i <= u*S && n-i >= 0){
//						tr("e", i, u*S-(n-i), u*S, n-i, f[x-u*S][i], px[u*S-(n-i)] * C(u*S, n-i, mod, fif));
						base += px[u*S-(n-i)] * C(u*S, n-i, mod, fif) % mod * f[x-u*S][i];
						base %= mod;
					}
				}
//				tr("BA", base, pow(26, x, mod));
				base = py[x] - base;
				if(base < 0)base += mod;
				out.println(base);
			}
		}
	}
	
	public static long pow(long a, long n, long mod) {
		//		a %= mod;
		long ret = 1;
		int x = 63 - Long.numberOfLeadingZeros(n);
		for (; x >= 0; x--) {
			ret = ret * ret % mod;
			if (n << 63 - x < 0)
				ret = ret * a % mod;
		}
		return ret;
	}

	
	public static long C(int n, int r, int mod, int[][] fif) {
		if (n < 0 || r < 0 || r > n)
			return 0;
		return (long) fif[0][n] * fif[1][r] % mod * fif[1][n - r] % mod;
	}

	
	long[] bin(int n, int a, int b, int[][] fif, int mod)
	{
		long[] ret = new long[n+1];
		for(int i = 0;i <= n;i++){
			ret[i] = (long)fif[0][n]*fif[1][i]%mod*fif[1][n-i]%mod;
		}
		long bb = 1;
		for(int i = 0;i < n;i++){
			ret[i] = ret[i] * bb % mod;
			bb = bb * b % mod;
		}
		long aa = 1;
		for(int i = n-1;i >= 0;i--){
			ret[i] = ret[i] * aa % mod;
			aa = aa * a % mod;
		}
		return ret;
	}
	
	public static int[][] enumFIF(int n, int mod) {
		int[] f = new int[n + 1];
		int[] invf = new int[n + 1];
		f[0] = 1;
		for (int i = 1; i <= n; i++) {
			f[i] = (int) ((long) f[i - 1] * i % mod);
		}
		long a = f[n];
		long b = mod;
		long p = 1, q = 0;
		while (b > 0) {
			long c = a / b;
			long d;
			d = a;
			a = b;
			b = d % b;
			d = p;
			p = q;
			q = d - c * q;
		}
		invf[n] = (int) (p < 0 ? p + mod : p);
		for (int i = n - 1; i >= 0; i--) {
			invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod);
		}
		return new int[][] { f, invf };
	}

	
	public static boolean inc(int[] a, int base) {
		int n = a.length;
		int i;
		for (i = n - 1; i >= 0 && a[i] == base - 1; i--)
			;
		if (i == -1)
			return false;

		a[i]++;
		Arrays.fill(a, i + 1, n, 0);
		return true;
	}

	
	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 C666().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)); }
}