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: Time Limit Exceeded)

using System;
using System.IO;
 
#region Program
namespace Program
{
    #region Solver
    public class Solver
    {
        static IO.StreamScanner
        sc = new IO.StreamScanner(Console.OpenStandardInput());
 
        static readonly string alp = "abcdefghijklmnopqrstuvwxyz";
 
        string s;
        int K;
 
        #region Solver
        public Solver()
        {
            s = sc.Scan();
            K = sc.Integer();
        }
        #endregion
 
        #region Solve
        public void Solve()
        {
            string ans = s;
            int enable = s.Length;
            int ope = K;
            for (int i = 0; i < s.Length; i++)
            {
                if (ope == 0) break;
                enable = enable - 1;
                int nowIdx = alp.IndexOf(s[i]);
                int idx = -1;
                if (enable == 0)
                {
                    idx =
                        nowIdx + ope < alp.Length ?
                            nowIdx + ope : (nowIdx + ope) % alp.Length;
                }
                else if (alp.Length - nowIdx - 1 < ope)
                {
                    idx = 0;
                    ope = ope - (alp.Length - nowIdx - 1) - 1;
                }
                if (0 <= idx)
                {
                    ans =
                        ans.Substring(0, i) + alp[idx] + ans.Substring(i + 1);
                }
            }
            Console.WriteLine(ans);
        }
        #endregion
    }
    #endregion
}
#endregion
 
#region Execute
class Execute
{
    public static void Main(string[] args)
    {
        new Program.Solver().Solve();
        Program.IO.Printer.Out.Flush();
    }
}
#endregion
 
#region Program.IO
namespace Program.IO
{
    using System.Text;
    using System.Globalization;
    using System.Linq;
    public class Printer : StreamWriter
    {
        static Printer()
        {
            Out = new Printer(Console.OpenStandardOutput())
            {
                AutoFlush = false
            };
        }
        public static Printer Out
        {
            get;
            set;
        }
        public override IFormatProvider FormatProvider
        {
            get
            {
                return CultureInfo.InvariantCulture;
            }
        }
        public Printer(System.IO.Stream stream)
            : base(stream, new UTF8Encoding(false, true))
        {
        }
        public Printer(System.IO.Stream stream, Encoding encoding)
            : base(stream, encoding)
        {
        }
        public void Write<T>(string format, T[] source)
        {
            base.Write(format, source.OfType<object>().ToArray());
        }
        public void WriteLine<T>(string format, T[] source)
        {
            base.WriteLine(format, source.OfType<object>().ToArray());
        }
    }
    public class StreamScanner
    {
        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;
        public StreamScanner(Stream stream)
        {
            str = stream;
        }
        private T[] enumerate<T>(int n, Func<T> f)
        {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f();
            return a;
        }
        public long Long()
        {
            if (isEof)
            {
                return long.MinValue;
            }
            long ret = 0;
            byte b = 0;
            var ng = false;
            do
            {
                b = read();
            }
            while (b != '-' && (b < '0' || '9' < b));
            if (b == '-')
            {
                ng = true;
                b = read();
            }
            for (; true; b = read())
            {
                if (b < '0' || '9' < b)
                {
                    return ng ? -ret : ret;
                }
                else ret = ret * 10 + b - '0';
            }
        }
        public long[] Long(int n)
        {
            return enumerate(n, Long);
        }
        public int Integer()
        {
            return (isEof) ? int.MinValue : (int)Long();
        }
        public int[] Integer(int n)
        {
            return enumerate(n, Integer);
        }
        public char[] Char(int n)
        {
            return enumerate(n, Char);
        }
        public char Char()
        {
            byte b = 0;
            do
            {
                b = read();
            }
            while ((b < 33 || 126 < b) && !isEof);
            return (char)b;
        }
        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
            {
                sb.Append(b);
            }
            return sb.ToString();
        }
        private byte read()
        {
            if (isEof)
            {
                return 0;
            }
            if (ptr >= len)
            {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }
    }
}
#endregion