Problem: There is a colony of villains with several holes aligned in a row, where each hole contains exactly one villain.

Each colony arrangement can be expressed as a string of even length, where the i-th character of the string represents the type of villain in the i-th hole. 

Iron Man can destroy a colony only if the colony arrangement is such that all villains of a certain type either live in the first half of the colony or in the second half of the colony.

His assistant Jarvis has a special power. It can swap villains of any two holes, i.e. swap any two characters in the string; he can do this operation any number of times.

Now Iron Man asks Jarvis q questions. In each question, he gives Jarvis two numbers x and y. Jarvis has to tell Iron Man the number of distinct colony arrangements he can create from the original one using his powers such that all villains having the same type as those originally living in x-th hole or y-th hole live in the same half and the Iron Man can destroy that colony arrangement.

Two colony arrangements are considered to be different if there exists a hole such that different types of villains are present in that hole in the arrangements.

Input

The first line contains a string s (2 ≤ |s| ≤ 10^{5}), representing the initial colony arrangement. String s can have both lowercase and uppercase English letters and its length is even.

The second line contains a single integer q (1 ≤ q ≤ 10^{5}) — the number of questions.

The i-th of the next q lines contains two integers x_i and y_i (1 ≤ x_i, y_i ≤ |s|, x_i ≠ y_i) — the two numbers given to the Jarvis for the i-th question.

Output

For each question output the number of arrangements possible modulo 10^9+7.

Examples

Input


abba
2
1 4
1 2


Output


2
0


Input


AAaa
2
1 2
1 3


Output


2
0


Input


abcd
1
1 3


Output


8

Note

Consider the first example. For the first question, the possible arrangements are "aabb" and "bbaa", and for the second question, index 1 contains 'a' and index 2 contains 'b' and there is no valid arrangement in which all 'a' and 'b' are in the same half.

Solution (in JAVA):

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

public class Main {
    void solve() {
        precompute(100000);
      char s[]=ns().toCharArray();
      int f[]=new int[53];
      int n=s.length;
      for(int i=1;i<=n;i++) f[get(s[i-1])]++;
      long dp[]=new long[n/2+1];
      long dp1[]=new long[n/2+1];
      long dp2[]=new long[n/2+1];
      dp[0]=1;
      for(int i=1;i<=52;i++){
          if(f[i]==0) continue;
          for(int j=n/2;j>=f[i];j--){
              dp[j]=add(dp[j],dp[j-f[i]]);
          }
      }
      long ans[][]=new long[53][53];
      for(int i=1;i<=52;i++){
          if(f[i]==0) continue;
          for(int j=0;j<=n/2;j++) dp1[j]=dp[j];
          for(int j=f[i];j<=n/2;j++){
              dp1[j]=sub(dp1[j],dp1[j-f[i]]);
          }
          for(int j=i+1;j<=52;j++){
              if(f[j]==0) continue;
              for(int k=0;k<=n/2;k++) dp2[k]=dp1[k];
              for(int k=f[j];k<=n/2;k++) dp2[k]=sub(dp2[k],dp2[k-f[j]]);
              ans[i][j]=ans[j][i]=dp2[n/2];
          }
      }
      long W=mul(fact[n/2],fact[n/2]);
        for(int i=1;i<=52;i++) W=mul(W,inv[f[i]]);

      int q=ni();
        while(q-->0){
            int x=ni(),y=ni();
            x=get(s[x-1]); y=get(s[y-1]);
            long ans2=0;
            if(x==y)ans2=mul(W,dp[n/2]);
            else ans2=mul(2,mul(W,ans[x][y]));
            pw.println(ans2);
        }

    }
    int get(char ch){
        if(ch>='a' && ch<='z') return ch-'a'+1;
        else return ch-'A'+27;
    }
    long add(long a,long b){
        a+=b;
        if(a>=M) a-=M;
        return a;
    }
    long sub(long a,long b){
        a-=b;
        if(a<0) a+=M;
        return a;
    }
    long mul(long a,long b){
        a*=b;
        if(a>=M) a%=M;
        return a;
    }
    long fact[];
    long inv[];
    void precompute(int n){
        fact=new long[n+1];
        inv=new long[n+1];
        fact[0]=1;
        for(int i=1;i<=n;i++) fact[i]=mul(fact[i-1],i);
        inv[n]=modInverse(fact[n],M);
        for(int i=n-1;i>=0;i--) inv[i]=mul(inv[i+1],i+1);


    }
    long modpow(long a, long b,long M)
    {
        long r=1;
        while(b>0)
        {
            if((b&1)>0) r=mul(r,a);
            a=mul(a,a);
            b>>=1;
        }
        return r;
    }

    long modInverse(long A, long M)
    {

        return modpow(A,M-2,M);
    }

    long M = (long)1e9+7;
    InputStream is;
    PrintWriter pw;
    String INPUT = "";

    void run() throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        pw = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        solve();
        pw.flush();
        if (!INPUT.isEmpty()) tr(System.currentTimeMillis() - s + "ms");

    }

    public static void main(String[] args) throws Exception {
        new Main().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 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 (INPUT.length() > 0) System.out.println(Arrays.deepToString(o));
    }

}