Problem:
Score : 400 points

Problem Statement

Mr. Takahashi has a string s consisting of lowercase English letters.
He repeats the following operation on s exactly K times.

Choose an arbitrary letter on s and change that letter to the next alphabet. Note that the next letter of z is a.

For example, if you perform an operation for the second letter on aaz, aaz becomes abz.
If you then perform an operation for the third letter on abz, abz becomes aba.

Mr. Takahashi wants to have the lexicographically smallest string after performing exactly K operations on s.
Find the such string.

Constraints

1≤|s|≤10^5

All letters in s are lowercase English letters.

1≤K≤10^9

Input

The input is given from Standard Input in the following format:

s
K

Output

Print the lexicographically smallest string after performing exactly K operations on s.

Sample Input 1

xyz
4

Sample Output 1

aya

For example, you can perform the following operations: xyz, yyz, zyz, ayz, aya.

Sample Input 2

a
25

Sample Output 2

z

You have to perform exactly K operations.

Sample Input 3

codefestival
100

Sample Output 3

aaaafeaaivap

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.concurrent.atomic.AtomicReference;

public class Main {

    final static boolean DEBUG = false;

    final void solve() throws Exception {
        char[] s = nextString().toCharArray();
        int k = nextInt();

        for (int i = 0; i < s.length; ++i) {
            if (s[i] != 'a' && 'z' - s[i] + 1 <= k) {
                k -= 'z' - s[i] + 1;
                s[i] = 'a';
            }
        }
        k %= 26;
        s[s.length - 1] += k;
        if (s[s.length - 1] > 'z') {
            s[s.length - 1] -= 26;
        }
        print(new String(s));
        println();
    }

    final static BufferedReader in;
    final static PrintWriter out;

    static final boolean isWhiteSpace(final int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == -1;
    }

    static final int read() throws Exception {
        return in.read();
    }

    static final int nextInt() throws Exception {
        int result = 0;
        boolean negative = false;
        int c = read();
        while (isWhiteSpace(c)) {
            c = read();
        }
        if (c == '-') {
            negative = true;
            c = read();
        }
        while (!isWhiteSpace(c)) {
            result = result * 10 + (c - '0');
            c = read();
        }
        return negative ? -result : result;
    }

    static final long nextLong() throws Exception {
        long result = 0;
        boolean negative = false;
        int c = read();
        while (isWhiteSpace(c)) {
            c = read();
        }
        if (c == '-') {
            negative = true;
            c = read();
        }
        while (!isWhiteSpace(c)) {
            result = result * 10 + (c - '0');
            c = read();
        }
        return negative ? -result : result;
    }

    static final StringBuilder tmpString = new StringBuilder(1 << 20);

    static final String nextString() throws Exception {
        tmpString.setLength(0);
        int c = read();
        while (isWhiteSpace(c)) {
            c = read();
        }
        while (!isWhiteSpace(c)) {
            tmpString.append((char) c);
            c = read();
        }
        return tmpString.toString();
    }

    static final char nextChar() throws Exception {
        int c = read();
        while (isWhiteSpace(c)) {
            c = read();
        }
        while (!isWhiteSpace(c)) {
            return (char) c;
        }
        return (char) 0;
    }

    static final String readLine() throws Exception {
        return in.readLine();
    }

    static final void print(final int i) {
        out.print(i);
    }

    static final void print(final long l) {
        out.print(l);
    }

    static final void print(final String s) {
        out.print(s);
    }

    static final void println() {
        out.println();
    }

    static {
        try {
            if (DEBUG) {
                String fileName = Main.class.getSimpleName();
                in = new BufferedReader(new FileReader(fileName + ".in"));
                out = new PrintWriter(new BufferedWriter(new FileWriter(fileName + ".out")));
            } else {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
            }
        } catch (Exception ex) {
            throw new RuntimeException(ex);
        }
    }

    static final AtomicReference<Exception> exs = new AtomicReference<Exception>();

    public static void main(String[] args) throws Exception {
        Thread th = new Thread(null, new Runnable() {
            @Override
            public void run() {
                try {
                    new Main().solve();
                    out.close();
                    return;
                } catch (Exception ex) {
                    exs.set(ex);
                }
            }
        }, "Test", 64 << 20);
        th.start();
        th.join();
        Exception ex = exs.get();
        if (ex != null) {
            throw ex;
        }
    }
}