Problem: Fibonacci strings are defined as follows: 

  * f1 = «a» 
  * f2 = «b» 
  * fn = fn - 1 fn - 2, n > 2



Thus, the first five Fibonacci strings are: "a", "b", "ba", "bab", "babba".

You are given a Fibonacci string and m strings si. For each string si, find the number of times it occurs in the given Fibonacci string as a substring.

Input

The first line contains two space-separated integers k and m — the number of a Fibonacci string and the number of queries, correspondingly.

Next m lines contain strings si that correspond to the queries. It is guaranteed that strings si aren't empty and consist only of characters "a" and "b".

The input limitations for getting 30 points are: 

  * 1 ≤ k ≤ 3000
  * 1 ≤ m ≤ 3000
  * The total length of strings si doesn't exceed 3000



The input limitations for getting 100 points are: 

  * 1 ≤ k ≤ 1018
  * 1 ≤ m ≤ 104
  * The total length of strings si doesn't exceed 105



Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.

Output

For each string si print the number of times it occurs in the given Fibonacci string as a substring. Since the numbers can be large enough, print them modulo 1000000007 (109 + 7). Print the answers for the strings in the order in which they are given in the input.

Examples

Input

6 5
a
b
ab
ba
aba


Output

3
5
3
3
1

Solution (in JAVA):

Solution:
//package abbyy2.easy;
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 G {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		char[] fb = new char[200000];
		fb[0] = 'b'; fb[1] = 'a';
		int b = 2, a = 1;
		while(b <= 100000){
			for(int i = 0;i < a;i++){
				fb[b+i] = fb[i];
			}
			int c = b + a;
			a = b; b = c;
		}
		
		int mod = 1000000007;
		int N = 4000;
		long[] f = new long[N];
		f[0] = f[1] = 1;
		for(int i = 2;i <= N-1;i++){
			f[i] = f[i-1] + f[i-2];
			if(f[i] >= mod)f[i] -= mod;
		}
		
		long[] na = new long[N+1];
		long[] nb = new long[N+1];
		long[] nab = new long[N+1];
		long[] nbb = new long[N+1];
		long[] nba = new long[N+1];
		na[0] = 1;
		nb[1] = 1;
		nba[2] = 1;
		for(int i = 2;i <= N;i++){
			na[i] = na[i-1] + na[i-2];
			nb[i] = nb[i-1] + nb[i-2];
			if(i >= 3){
				nab[i] = nab[i-1] + nab[i-2] + (i%2==1?1:0);
				nbb[i] = nbb[i-1] + nbb[i-2] + (i%2==0?1:0);
				nba[i] = nba[i-1] + nba[i-2];
				
				nab[i] %= mod;
				nbb[i] %= mod;
				nba[i] %= mod;
			}
			na[i] %= mod; nb[i] %= mod;
		}
		
		int n = ni()-1;
		int z = ni();
		for(int r = 0;r < z;r++){
			char[] s = ns().toCharArray();
			long ret = 0;
			if(n == 0){
				if(s.length == 1 && s[0] == 'a'){
					ret = 1;
				}else{
					ret = 0;
				}
			}else if(s.length == 1){
				if(s[0] == 'a'){
					ret = na[n];
				}else{
					ret = nb[n];
				}
			}else{
				int[] kmp = kmpTable(s);
				int ind = Arrays.binarySearch(f, 1, 30, s.length);
				if(ind < 0)ind = -ind-1;
				int o = ind;
				if(n <= ind){
					ret = count(kmp, s, Arrays.copyOf(fb, (int)f[n])) % mod;
				}else{
					long ca = count(kmp, s, Arrays.copyOf(fb, (int)f[o]));
					long cb = count(kmp, s, Arrays.copyOf(fb, (int)f[o+1]));
					
					char[] ab = new char[(int)(f[o]+f[o+1])];
					System.arraycopy(fb, 0, ab, 0, (int)f[o]);
					System.arraycopy(fb, 0, ab, (int)f[o], (int)f[o+1]);
					long cab = count(kmp, s, ab) - ca - cb;
					
					char[] ba = new char[(int)(f[o]+f[o+1])];
					System.arraycopy(fb, 0, ba, 0, (int)f[o+1]);
					System.arraycopy(fb, 0, ba, (int)f[o+1], (int)f[o]);
					long cba = count(kmp, s, ba) - ca - cb;
					
					char[] bb = new char[(int)(f[o+1]+f[o+1])];
					System.arraycopy(fb, 0, bb, 0, (int)f[o+1]);
					System.arraycopy(fb, 0, bb, (int)f[o+1], (int)f[o+1]);
					long cbb = count(kmp, s, bb) - cb - cb;
					
					ret = (
							ca * na[n-ind] % mod
							+ cb * nb[n-ind] % mod
							+ cab * nab[n-ind] % mod
							+ cbb * nbb[n-ind] % mod
							+ cba * nba[n-ind] % mod
							+ 5L*mod
							) % mod;
				}
			}
			out.println(ret);
		}
	}
	
	static int count(int[] kmp, char[] q, char[] h)
	{
		int p = 0;
		int hit = 0;
		for(char element : h){
			while(p >= 0 && q[p] != element)p = kmp[p];
			if(++p == q.length){
				hit++;
				p = kmp[p];
			}
		}
		return hit;
	}
	
	public static int[] kmpTable(char[] str)
	{
		int n = str.length;
		int[] kmp = new int[n+1];
		kmp[0] = -1; kmp[1] = 0;
		for(int i = 2, j = 0;i <= n;i++){
			while(j > 0 && str[i-1] != str[j])j = kmp[j];
			kmp[i] = str[i-1] == str[j] ? ++j : 0;
		}
		return kmp;
	}
	
	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 G().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)); }
}