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: Accepted)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Net;
using static System.Console;
using static System.Math;
using static CS_Contest.Utils;
//using static CS_Contest.Library;

namespace CS_Contest {
	using Li = List<int>;
	using LLi = List<List<int>>;
	using Ll = List<long>;

	internal class Program {
		private static void Main(string[] args) {
			var sw = new StreamWriter(OpenStandardOutput()) { AutoFlush = false };
			SetOut(sw);
			new Calc().Solve();
			Out.Flush();
		}
		

		private class Calc {

			public void Solve() {
				var s = ReadLine().ToArray();
				var K = ReadInt();
				var ranges = new int[s.Length];
				foreach (var t in s.ToIndexEnumerable()) {
					var add = 0;
					if (t.Value > 'a') add = 'z' - t.Value + 1;
					ranges[t.Index] = add;
				}

				for (var i = 0; i < s.Length; i++) {
					if (K < ranges[i]) continue;
					K -= ranges[i];
					ranges[i] = 0;
					s[i] = 'a';
				}
				K %= 26;
				s[s.Length - 1] = (char) ((s[s.Length-1] + K));
				s.StringJoin().WL();
				return;
			}
		}
	}

	public static class Utils {
		public static int ModValue = (int)(1000000007);
		public static long INF = long.MaxValue;

		public static long Mod(long x) => x % ModValue;

		public static long ModPow(long x, long n) {
			long tmp = 1; while (n != 0) { if (n % 2 == 1) { tmp = Mod(tmp * x); } x = Mod(x * x); n /= 2; }
			return tmp;
		}

		public static long DivMod(long x, long y) => Mod(x * ModPow(y, (long)(1e9 + 5)));

		public static void WL(this object obj) => WriteLine(obj);

		public static void WL(this string obj) => WriteLine(obj);

		public static void WL<T>(this IEnumerable<T> list) => list.ToList().ForEach(x => x.WL());

		public static int ReadInt() => int.Parse(ReadLine());

		public static List<int> ReadInts(char s = ' ') => ReadLine().Split(s).Where(x => x != "").Select(int.Parse).ToList();

		public static long ReadLong() => long.Parse(ReadLine());

		public static List<long> ReadLongs(char s = ' ') => ReadLine().Split(s).Select(long.Parse).ToList();

		public static void ReadMulti(out int x, out int y) {
			var i = ReadInts(' ');
			x = i[0]; y = i[1];
		}

		public static void ReadMulti(out long x, out long y) {
			var i = ReadLongs(' ');
			x = i[0]; y = i[1];
		}

		public static void ReadMulti(out int x, out int y, out int z) {
			var i = ReadInts(' ');
			x = i[0]; y = i[1]; z = i[2];
		}

		public static void ReadMulti(out int x, out int y, out int z, out int v) {
			var i = ReadInts(' ');
			x = i[0]; y = i[1]; z = i[2]; v = i[3];
		}

		public static string StringJoin<T>(this IEnumerable<T> l, string separator = "") => string.Join(separator, l);

		public static long GCD(long m, long n) {
			long tmp;
			if (m < n) { tmp = n; n = m; m = tmp; }
			while (m % n != 0) {
				tmp = n;
				n = m % n;
				m = tmp;
			}
			return n;
		}

		public static long LCM(long m, long n) => m * (n / GCD(m, n));

		public static void REP(int n, Action<int> act) {
			for (var i = 0; i < n; i++) {
				act(i);
			}
		}

		public static void RREP(int n, Action<int> act) {
			for (var i = n - 1; i >= 0; i--) {
				act(i);
			}
		}

		public static void Yes() => "Yes".WL();

		public static void No() => "No".WL();

		public static void YES() => "YES".WL();

		public static void NO() => "NO".WL();

		public static int ManhattanDistance(int x1, int y1, int x2, int y2) => Abs(x2 - x1) + Abs(y2 - y1);

		public struct IndexT<T> {
			public T Value { get; set; }
			public int Index { get; set; }

			public IndexT(T v, int i) {
				Value = v; Index = i;
			}
			public override string ToString() {
				return Value + " " + Index;
			}
		}

		public static IEnumerable<IndexT<T>> ToIndexEnumerable<T>(this IEnumerable<T> list) => list.Select((x, i) => new IndexT<T>(x, i));

		public static Queue<T> ToQueue<T>(this IEnumerable<T> iEnumerable) {
			var rt = new Queue<T>();
			foreach (var item in iEnumerable) {
				rt.Enqueue(item);
			}
			return rt;
		}

		public static IndexT<T> IndexOfMin<T>(this IEnumerable<T> ie) where T : IComparable<T>
			=> ie.ToIndexEnumerable().Aggregate((src, acu) => (src.Value.CompareTo(acu.Value) < 0) ? src : acu);

		public static Tuple<TKey, TSource> ToTuple<TKey, TSource>(this KeyValuePair<TKey, TSource> kvp) => new Tuple<TKey, TSource>(kvp.Key, kvp.Value);

		public static IEnumerable<Tuple<TKey, TSource>> ToTupleList<TKey, TSource>(this Dictionary<TKey, TSource> d) => d.Select(_ => _.ToTuple());
	}
}