Problem:
Score : 1100 points

Problem Statement

We will call a string that can be obtained by concatenating two equal strings an even string.
For example, xyzxyz and aaaaaa are even, while ababab and xyzxy are not.

For a non-empty string S, we will define f(S) as the shortest even string that can be obtained by appending one or more characters to the end of S.
For example, f(abaaba)=abaababaab.
It can be shown that f(S) is uniquely determined for a non-empty string S.

You are given an even string S consisting of lowercase English letters.
For each letter in the lowercase English alphabet, find the number of its occurrences from the l-th character through the r-th character of f^{10^{100}} (S).

Here, f^{10^{100}} (S) is the string f(f(f( ... f(S) ... ))) obtained by applying f to S 10^{100} times.

Constraints

2 \leq |S| \leq 2\times 10^5

1 \leq l \leq r \leq 10^{18}

S is an even string consisting of lowercase English letters.

l and r are integers.

Input

Input is given from Standard Input in the following format:

S
l r

Output

Print 26 integers in a line with spaces in between.
The i-th integer should be the number of the occurrences of the i-th letter in the lowercase English alphabet from the l-th character through the r-th character of f^{10^{100}} (S).

Sample Input 1

abaaba
6 10

Sample Output 1

3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Since f(abaaba)=abaababaab, the first ten characters in f^{10^{100}}(S) is also abaababaab. Thus, the sixth through the tenth characters are abaab. In this string, a appears three times, b appears twice and no other letters appear, and thus the output should be 3 and 2 followed by twenty-four 0s.

Sample Input 2

xx
1 1000000000000000000

Sample Output 2

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1000000000000000000 0 0

Sample Input 3

vgxgpuamkvgxgvgxgpuamkvgxg
1 1000000000000000000

Sample Output 3

87167725689669676 0 0 0 0 0 282080685775825810 0 0 0 87167725689669676 0 87167725689669676 0 0 87167725689669676 0 0 0 0 87167725689669676 141040342887912905 0 141040342887912905 0 0

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Text;
using System.Collections.Generic;
using System.Linq;
class Solve{
    public Solve(){}
    StringBuilder sb;
    public static int Main(){
        new Solve().Run();
        return 0;
    }
    void Run(){
        sb = new StringBuilder();
        Calc();
        Console.Write(sb.ToString());
    }
    void Calc(){
        string s = Console.ReadLine();
        SuffixArray S = new SuffixArray(s);
        int d = s.Length;
        int N = s.Length;
        for(int i=1;i<s.Length;i++){
            if(S.SameSize(0,i) == N-i){
                d = i;
                break;
            }
        }
        string[] str = Console.ReadLine().Split(' ');
        long L = long.Parse(str[0]);
        long R = long.Parse(str[1]);
        int l = (int)(L%d)-1;
        int r = (int)(R%d)+1;
        long D = (R-L+1+l+r)/d;
        long[] A = new long[26];
        long[] B = new long[26];
        long[] C = new long[26];
        for(int i=0;i<d;i++){
            if(i <= l){
                A[s[i]-'a']++;
            }
            B[s[i]-'a']++;
            if(i >= r){
                C[s[i]-'a']++;
            }
        }
        for(int i=0;i<26;i++){
            long count = 0;
            count = D*B[i]-A[i]-C[i];
            sb.Append(count);
            if(i != 25){
                sb.Append(" ");
            }
            else{
                sb.Append("\n");
            }
        }
    }
}
public class SuffixArray{
    List<int[]> a;
    int size;
    public SuffixArray(string s){
        a = new List<int[]>();
        int[] b = new int[s.Length];
        {
            int[] c = new int[s.Length];
            for(int i=0;i<s.Length;i++){
                c[i] = i;
            }
            Array.Sort(c,(x,y) => s[x] > s[y] ? 1 : (s[x] == s[y] ? 0 : -1));
            int count = 0;
            b[c[0]] = 0;
            for(int i=1;i<s.Length;i++){
                if(s[c[i-1]] != s[c[i]]){
                    count++;
                }
                b[c[i]] = count;
            }
        }
        a.Add(b);
        int l;
        for(l=2;l<s.Length;l*=2){
            int[] c = new int[s.Length-l+1];
            for(int i=0;i<s.Length-l+1;i++){
                c[i] = i;
            }
            Array.Sort(c,(x,y) => b[x] > b[y] ? 1 : (b[x] == b[y] ? b[x+l/2] - b[y+l/2] : -1));
            int count = 0;
            int[] b0 = new int[s.Length-l+1];
            b0[c[0]] = 0;
            for(int i=1;i<s.Length-l+1;i++){
                if(b[c[i-1]] != b[c[i]] || b[c[i-1]+l/2] != b[c[i]+l/2]){
                    count++;
                }
                b0[c[i]] = count;
            }
            a.Add(b0);
            b = b0;
        }
        size = l/2;
    }
    public int SameSize(int x,int y){
        int x0 = x;
        int y0 = y;
        int count = 0;
        int p = a.Count-1;
        for(int l=size;l!=0;l/=2,p--){
            if(x0 < a[p].Length && y0 < a[p].Length && a[p][x0] == a[p][y0]){
                count += l;
                x0 += l;
                y0 += l;
            }
        }
        return count;
    }
    public int SameSizeRev(int x,int y){
        int x0 = x;
        int y0 = y;
        int count = 0;
        int p = a.Count-1;
        for(int l=size;l!=0;l/=2,p--){
            if(x0 >= l-1 && y0 >= l-1 && a[p][x0-l+1] == a[p][y0-l+1]){
                count += l;
                x0 -= l;
                y0 -= l;
            }
        }
        return count;
    }
}