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

using System;
using System.Collections;
using System.Collections.Generic;
using System.Dynamic;
using System.IO;
using System.Linq;
using System.Linq.Expressions;
using System.Reflection.Emit;
using System.Runtime.Remoting.Proxies;
using System.Text;
using static System.Console;
using static System.Math;
using static Ex;
using static ArrayEx;
class AC {
    /*------------------------------------------------------------------*/
    string s;
    int K;
    void Solve() {
        io.i(out s, out K);

        var S = s.ToCharArray();
        var headIdx = 0;
        var left = K;

        while (true) {
            if (headIdx < s.Length - 1) {
                var d = dis(S[headIdx]);
                if (d <= left) {
                    S[headIdx] = 'a';
                    left -= d;
                }
                headIdx++;
            } else {
                S[S.Length - 1] = update(S[S.Length - 1], left);
                break;
            }
        }
        io.o(new string(S));
    }

    int dis(char c) => 'z' - c + 1;
    char update(char c, int cnt) {
        var alp = 'z' - 'a' + 1;
        var C = c - 'a';
        C += cnt;
        C %= alp;
        C += 'a';
        return (char)C;
    }

    /*------------------------------------------------------------------*/
    void Test() {
        //--- TEST ---//
    }
    public static void Main(string[] args) => new AC().Stream();
    IO io = new IO();
    private void Stream() {
        /*
        var exStdIn = new System.IO.StreamReader("stdin.txt");
        SetIn(exStdIn);
        Test();
        */
        Solve();
        io.Flush();
    }
}

#region OTHER
class IO {
    #region INPUT
    private const int Size = 1 << 12;
    private readonly Stream _stream = OpenStandardInput();
    private readonly byte[] _buffer = new byte[Size];
    private int _ptr = 0, _buffLen = 0;
    private bool HasNextByte() {
        if (_ptr < _buffLen)
            return true;
        _ptr = 0;
        _buffLen = _stream.Read(_buffer, 0, Size);
        return _buffLen > 0;
    }
    private byte ReadByte() {
        if (HasNextByte())
            return _buffer[_ptr++];
        else
            //inputの末尾の改行がないとerror
            throw new EndOfStreamException();

    }
    private bool IsAscii(int c) => '!' <= c && c <= '~';
    private char NextChar() {
        byte b = 0;
        do
            b = ReadByte(); while (!IsAscii(b));
        return (char)b;
    }
    private string Next() {
        var sb = new StringBuilder();
        for (var b = NextChar(); IsAscii(b); b = (char)ReadByte())
            sb.Append(b);
        return sb.ToString();
    }
    private void Read<T>(out T v) => v = SuitType<T>(Next());
    private bool TypeEqual<T, TU>() => typeof(T) == typeof(TU);
    private T SuitType<T>(string s) {
        if (TypeEqual<T, int>())
            ConvertType<T, int>(int.Parse(s));
        if (TypeEqual<T, long>())
            ConvertType<T, long>(long.Parse(s));
        if (TypeEqual<T, double>())
            ConvertType<T, double>(double.Parse(s));
        if (TypeEqual<T, char>())
            ConvertType<T, char>(char.Parse(s));
        return ConvertType<T, string>(s);
    }
    private T i<T>() => SuitType<T>(String);
    public string String => Next();
    public char Char => NextChar();
    public int Int => int.Parse(Next());
    public long Long => long.Parse(Next());
    public double Double => double.Parse(Next());
    public void i<T>(out T v) => Read(out v);
    public void i<T, TU>(out T t, out TU u) {
        i(out t);
        i(out u);
    }
    public void i<T, TU, TV>(out T t, out TU u, out TV v) {
        i(out t, out u);
        i(out v);
    }
    public void i<T, TU, TV, TW>(out T t, out TU u, out TV v, out TW w) {
        i(out t, out u);
        i(out v, out w);
    }
    public void i<T, TU, TV, TW, TX>(out T t, out TU u, out TV v, out TW w, out TX x) {
        i(out t, out u, out v);
        i(out w, out x);
    }
    public void i<T, TU, TV, TW, TX, TY>(out T t, out TU u, out TV v, out TW w, out TX x, out TY y) {
        i(out t, out u, out v);
        i(out w, out x, out y);
    }
    public void ini<T>(out T[] a, int n) {
        a = new T[n];
        for (int i = 0; i < n; ++i)
            a[i] = i<T>();
    }
    public void ini<T, TU>(out T[] a, out TU[] b, int n) {
        a = new T[n];
        b = new TU[n];
        for (int i = 0; i < n; ++i) {
            a[i] = i<T>();
            b[i] = i<TU>();
        }
    }
    public void ini<T, TU, TV>(out T[] a, out TU[] b, out TV[] c, int n) {
        a = new T[n];
        b = new TU[n];
        c = new TV[n];
        for (int i = 0; i < n; ++i) {
            a[i] = i<T>();
            b[i] = i<TU>();
            c[i] = i<TV>();
        }
    }
    public void ini<T>(out T[,] a, int h, int w) {
        a = new T[h, w];
        for (int i = 0; i < h; ++i)
            for (int j = 0; j < w; ++j)
                a[i, j] = i<T>();
    }
    #endregion
    #region OUTPUT
    private readonly StreamWriter _sw = new StreamWriter(OpenStandardOutput()) {
#if DEBUG
        AutoFlush = true
#else
        AutoFlush = false
#endif
    };
    public void Flush() => Console.Out.Flush();
    public void o(params Object[] xs) => Print(false, xs);
    public void o_(params Object[] xs) => Print(true, xs);
    private void Print(bool isOneLine, params Object[] xs) {
        foreach (var x in xs) {
            if (x is int[])
                PrintArr<int>(isOneLine, x);
            else if (x is long[])
                PrintArr<int>(isOneLine, x);
            else if (x is double[])
                PrintArr<int>(isOneLine, x);
            else if (x is char[])
                PrintArr<int>(isOneLine, x);
            else if (x is string[])
                PrintArr<int>(isOneLine, x);
            else if (x is bool[])
                PrintArr<int>(isOneLine, x);
            else if (x is int[,])
                PrintArr2D(ConvertType<int[,], object>(x));
            else if (x is long[,])
                PrintArr2D(ConvertType<long[,], object>(x));
            else if (x is double[,])
                PrintArr2D(ConvertType<double[,], object>(x));
            else if (x is char[,])
                PrintArr2D(ConvertType<char[,], object>(x));
            else if (x is string[,])
                PrintArr2D(ConvertType<string[,], object>(x));
            else if (x is bool[,])
                PrintArr2D(ConvertType<bool[,], object>(x));
            else
                WriteLine(x);
        }
    }
    private void PrintArr2D<T>(T[,] a) {
        int a0 = a.GetLength(0), a1 = a.GetLength(1);
        for (int i = 0; i < a0; ++i) {
            for (int j = 0; j < a1 - 1; ++j)
                Write(a[i, j] + " ");
            WriteLine(a[i, a1 - 1]);
        }
    }
    private void PrintArr<T>(bool isOneLine, Object xs) {
        if (isOneLine)
            PrintArr1D_(ConvertType<T[], object>(xs));
        else
            PrintArr1D(ConvertType<T[], object>(xs));
    }
    private void PrintArr1D<T>(T[] xs) {
        foreach (var x in xs)
            WriteLine(x);
    }
    private void PrintArr1D_<T>(T[] xs) => WriteLine(string.Join(" ", xs));
    public void YN(bool f) => WriteLine(f ? "YES" : "NO");
    public void Yn(bool f) => WriteLine(f ? "Yes" : "No");
    public void yn(bool f) => WriteLine(f ? "yes" : "no");
    #endregion
    private T ConvertType<T, TU>(TU v) => (T)Convert.ChangeType(v, typeof(T));
    public IO() { SetOut(_sw); }
}
static class Ex {
    public static void REP(int a, Action<int> act) => FOR(0, a, act);
    public static void FOR(int a, int b, Action<int> act) => FOR(a, b, 1, act);
    public static void FOR(int a, int b, int n, Action<int> act) {
        for (int i = a; i < b; i += n)
            act(i);
    }
    public static void REPEQ(int a, Action<int> act) => FOR(0, a + 1, act);
    public static void FOREQ(int a, int b, Action<int> act) => FOR(a, b + 1, act);
    public static void FOREQ(int a, int b, int n, Action<int> act) => FOR(a, b + 1, n, act);
    public static T MIN<T>(params T[] a) => a.Min();
    public static T MAX<T>(params T[] a) => a.Max();
}
static class NumEx {
    public static string toString(this double d) => d.ToString("R");
    public static string Pad0<T>(this T s, int n) => s.ToString().PadLeft(n, '0');
    public static int RoundOff(this double v, int n) => (int)Round(v, n - 1, MidpointRounding.AwayFromZero);
    public static int RoundUp(this double v) => (int)Ceiling(v);
    public static int RoundDown(this double v) => (int)Floor(v);
    public static bool Odd(this int v) => (v & 1) != 0;
    public static bool Odd(this long v) => (v & 1) != 0;
}
static class ArrayEx {
    public static void SET<T>(this T[] a, T v) {
        for (int i = 0; i < a.Length; ++i)
            a[i] = v;
    }
    public static void SET<T>(this T[,] a, T v) {
        for (int i = 0; i < a.GetLength(0); ++i)
            for (int j = 0; j < a.GetLength(1); ++j)
                a[i, j] = v;
    }
    public static IEnumerable<T> UNFOLD<T>(Func<int, T> func) => UNFOLD(0, func);
    public static IEnumerable<T> UNFOLD<T>(int s, Func<int, T> func) {
        while (true)
            yield return func(s++);
    }
    public static void ITER<T>(this IEnumerable<T> xs, Action<T> act) {
        foreach (var x in xs) act(x);
    }
}
#endregion