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.Generic;
using System.Linq;
using System.IO;

class Program
{
    const int M = 1000000007;
    const double eps = 1e-9;
    static int[] dd = { 0, 1, 0, -1, 0 };
    static void Main()
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        var sc = new Scan();
        var s = sc.Str;
        int k = sc.Int;
        int cnt = 0;
        string ans = "";
        for (int i = 0; i < s.Length; i++)
        {
            cnt += ('a' + 26 - s[i]) % 26;
            if (cnt > k)
            {
                int c2 = k - cnt + ('a' + 26 - s[i]) % 26;
                for (int j = i; j < s.Length; j++)
                {
                    if (j == s.Length - 1)
                    {
                        ans += (char)(s[j] + c2 % 26);
                    }
                    else if (('a' + 26 - s[j]) % 26 <= c2)
                    {
                        ans += "a";
                        c2 -= ('a' + 26 - s[j]) % 26;
                    }
                    else
                    {
                        ans += (char)s[j];
                    }
                }
                DBG(ans);
                return;
            }
            if (i == s.Length - 1)
            {
                ans += (char)('a' + (k - cnt) % 26);
            }
            else
                ans += "a";
        }
        sw.WriteLine(ans);
        sw.Flush();
    }

    static void swap<T>(ref T a, ref T b) { var t = a; a = b; b = t; }
    static void swap<T>(IList<T> a, int i, int j) { var t = a[i]; a[i] = a[j]; a[j] = t; }
    static T Max<T>(params T[] a) { return a.Max(); }
    static T Min<T>(params T[] a) { return a.Min(); }
    static void DBG<T>(params T[] a) { Console.WriteLine(string.Join(" ", a)); }
    static void DBG(params object[] a) { Console.WriteLine(string.Join(" ", a)); }
    static T[] copy<T>(IList<T> a)
    {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
}
class Scan
{
    public int Int { get { return int.Parse(Str); } }
    public long Long { get { return long.Parse(Str); } }
    public double Double { get { return double.Parse(Str); } }
    public string Str { get { return Console.ReadLine().Trim(); } }
    public int[] IntArr { get { return StrArr.Select(int.Parse).ToArray(); } }
    public int[] IntArrWithSep(char sep) { return Str.Split(sep).Select(int.Parse).ToArray(); }
    public long[] LongArr { get { return StrArr.Select(long.Parse).ToArray(); } }
    public double[] DoubleArr { get { return StrArr.Select(double.Parse).ToArray(); } }
    public string[] StrArr { get { return Str.Split(); } }
    T cv<T>(string inp)
    {
        if (typeof(T).Equals(typeof(int)))    return (T)Convert.ChangeType(int.Parse(inp), typeof(T));
        if (typeof(T).Equals(typeof(long)))   return (T)Convert.ChangeType(long.Parse(inp), typeof(T));
        if (typeof(T).Equals(typeof(double))) return (T)Convert.ChangeType(double.Parse(inp), typeof(T));
        if (typeof(T).Equals(typeof(char)))   return (T)Convert.ChangeType(inp[0], typeof(T));
        return (T)Convert.ChangeType(inp, typeof(T));
    }
    public void Multi<T>(out T a) { a = cv<T>(Str); }
    public void Multi<T, U>(out T a, out U b)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); }
    public void Multi<T, U, V>(out T a, out U b, out V c)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); }
    public void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); }
    public void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); }
}
class mymath
{
    static int Mod = 1000000007;
    public void setMod(int m) { Mod = m; }
    public bool isprime(long a)
    {
        if (a < 2) return false;
        for (long i = 2; i * i <= a; i++) if (a % i == 0) return false;
        return true;
    }
    public bool[] sieve(int n)
    {
        var isp = new bool[n + 1];
        for (int i = 2; i <= n; i++) isp[i] = true;
        for (int i = 2; i * i <= n; i++) if (isp[i]) for (int j = i * i; j <= n; j += i) isp[j] = false;
        return isp;
    }
    public List<int> getprimes(int n)
    {
        var prs = new List<int>();
        var isp = sieve(n);
        for (int i = 2; i <= n; i++) if (isp[i]) prs.Add(i);
        return prs;
    }
    public long[][] E(int n)
    {
        var ret = new long[n][];
        for (int i = 0; i < n; i++)
        {
            ret[i] = new long[n];
            ret[i][i] = 1;
        }
        return ret;
    }
    public long[][] powmat(long[][] A, long n)
    {
        if (n == 0) return E(A.Length);
        var t = powmat(A, n / 2);
        if ((n & 1) == 0) return mulmat(t, t);
        return mulmat(mulmat(t, t), A);
    }
    public long[] mulmat(long[][] A, long[] x)
    {
        int n = A.Length, m = x.Length;
        var ans = new long[n];
        for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) ans[i] = (ans[i] + x[j] * A[i][j]) % Mod;
        return ans;
    }
    public long[][] mulmat(long[][] A, long[][] B)
    {
        int n = A.Length, m = B[0].Length, l = B.Length;
        var ans = new long[n][];
        for (int i = 0; i < n; i++)
        {
            ans[i] = new long[m];
            for (int j = 0; j < m; j++) for (int k = 0; k < l; k++) ans[i][j] = (ans[i][j] + A[i][k] * B[k][j]) % Mod;
        }
        return ans;
    }
    public long[] addmat(long[] x, long[] y)
    {
        int n = x.Length;
        var ans = new long[n];
        for (int i = 0; i < n; i++) ans[i] = (x[i] + y[i]) % Mod;
        return ans;
    }
    public long[][] addmat(long[][] A, long[][] B)
    {
        int n = A.Length, m = A[0].Length;
        var ans = new long[n][];
        for (int i = 0; i < n; i++) ans[i] = addmat(A[i], B[i]);
        return ans;
    }
    public long powmod(long a, long b)
    {
        if (a >= Mod) return powmod(a % Mod, b);
        if (a == 0) return 0;
        if (b == 0) return 1;
        var t = powmod(a, b / 2);
        if ((b & 1) == 0) return t * t % Mod;
        return t * t % Mod * a % Mod;
    }
    public long inv(long a) { return powmod(a, Mod - 2); }
    public long gcd(long a, long b)
    {
        while (b > 0) { var t = a % b; a = b; b = t; }
        return a;
    }
    public long lcm(long a, long b) { return a * (b / gcd(a, b)); }
    public long Comb(int n, int r)
    {
        if (n < 0 || r < 0 || r > n) return 0;
        if (n - r < r) r = n - r;
        if (r == 0) return 1;
        if (r == 1) return n;
        var numerator = new int[r];
        var denominator = new int[r];
        for (int k = 0; k < r; k++)
        {
            numerator[k] = n - r + k + 1;
            denominator[k] = k + 1;
        }
        for (int p = 2; p <= r; p++)
        {
            int pivot = denominator[p - 1];
            if (pivot > 1)
            {
                int offset = (n - r) % p;
                for (int k = p - 1; k < r; k += p)
                {
                    numerator[k - offset] /= pivot;
                    denominator[k] /= pivot;
                }
            }
        }
        long result = 1;
        for (int k = 0; k < r; k++) if (numerator[k] > 1) result = result * numerator[k] % Mod;
        return result;
    }
}