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.*;

/**
 * @author baito
 */

public class Main
{
    static StringBuilder sb = new StringBuilder();
    static FastScanner sc = new FastScanner(System.in);
    static int INF = 12345678;
    static long LINF = 123456789123456789L;
    static long MINF = -123456789123456789L;
    static long MOD = 1000000007;
    static int[] y4 = {0, 1, 0, -1};
    static int[] x4 = {1, 0, -1, 0};
    static int[] y8 = {0, 1, 0, -1, -1, 1, 1, -1};
    static int[] x8 = {1, 0, -1, 0, 1, -1, 1, -1};
    static long[] F;//factorial
    static boolean[] isPrime;
    static int[] primes;
    static char[][] map;

    static int N, M;
    static int[] X;


    public static void main(String[] args)
    {
        char[] s = sc.next().toCharArray();
        int K = sc.nextInt();
        N = s.length;
        int i = 0;
        while (K != 0)
        {
            int need = needsToA(s[i]);
            if (i >= N - 1)
            {
                K %= 26;//todo
                int yutori = 'z' - s[i];
                if (yutori + 1 <= K)
                {
                    //aになったとき
                    K -= yutori + 1;
                    s[i] = (char) ('a' + K);
                }
                else
                {
                    s[i] += K;
                }
                break;
            }
            if (s[i] == 'a')
            {
                i++;
                continue;
            }

            if (K >= need)
            {
                K -= need;
                s[i] = 'a';
            }
            i++;
        }
        for (int j = 0; j < N; j++)
        {
            System.out.print(s[j]);
        }
        System.out.println("");
    }

    public static int needsToA(char c)
    {
        return 'z' - c + 1;
    }

    public static long getHashKey(int a, int b)
    {
        return (long) a << 32 | b;
    }

    public static boolean isOutofIndex(int x, int y)
    {
        if (x < 0 || y < 0) return true;
        if (map[0].length <= x || map.length <= y) return true;
        return false;
    }

    public static void setPrimes()
    {
        int n = 100001;
        isPrime = new boolean[n];
        List<Integer> prs = new ArrayList<>();
        Arrays.fill(isPrime, true);
        isPrime[0] = isPrime[1] = false;
        for (int i = 2; i * i <= n; i++)
        {
            if (!isPrime[i]) continue;
            prs.add(i);
            for (int j = i * 2; j < n; j += i)
            {
                isPrime[j] = false;
            }
        }
        primes = new int[prs.size()];
        for (int i = 0; i < prs.size(); i++)
            primes[i] = prs.get(i);
    }

    public static void revSort(int[] a)
    {
        Arrays.sort(a);
        reverse(a);
    }

    public static void revSort(long[] a)
    {
        Arrays.sort(a);
        reverse(a);
    }

    public static int[][] copy(int[][] ar)
    {
        int[][] nr = new int[ar.length][ar[0].length];
        for (int i = 0; i < ar.length; i++)
            for (int j = 0; j < ar[0].length; j++)
                nr[i][j] = ar[i][j];
        return nr;
    }


    /**
     * <h1>指定した値以上の先頭のインデクスを返す</h1>
     * <p>配列要素が０のときは、０が返る。</p>
     *
     * @return<b>int</b> ： 探索した値以上で、先頭になるインデクス
     */
    public static int lowerBound(final int[] arr, final int value)
    {
        int low = 0;
        int high = arr.length;
        int mid;
        if (arr[high - 1] < value)
        {
            return -1;
        }
        while (low < high)
        {
            mid = ((high - low) >>> 1) + low;    //(low + high) / 2 (オーバーフロー対策)
            if (arr[mid] < value)
            {
                low = mid + 1;
            }
            else
            {
                high = mid;
            }
        }
        return low;
    }

    /**
     * <h1>指定した値より大きい先頭のインデクスを返す</h1>
     * <p>配列要素が０のときは、０が返る。</p>
     *
     * @return<b>int</b> ： 探索した値より上で、先頭になるインデクス
     */
    public static int upperBound(final int[] arr, final int value)
    {
        int low = 0;
        int high = arr.length;
        int mid;
        if (arr[high - 1] <= value)
        {
            return -1;
        }
        while (low < high)
        {
            mid = ((high - low) >>> 1) + low;    //(low + high) / 2 (オーバーフロー対策)
            if (arr[mid] <= value)
            {
                low = mid + 1;
            }
            else
            {
                high = mid;
            }
        }
        return low;
    }

    //次の順列に書き換える、最大値ならfalseを返す
    public static boolean nextPermutation(int A[])
    {
        int len = A.length;
        int pos = len - 2;
        for (; pos >= 0; pos--)
        {
            if (A[pos] < A[pos + 1]) break;
        }
        if (pos == -1) return false;

        //posより大きい最小の数を二分探索
        int ok = pos + 1;
        int ng = len;
        while (Math.abs(ng - ok) > 1)
        {
            int mid = (ok + ng) / 2;
            if (A[mid] > A[pos]) ok = mid;
            else ng = mid;

        }

        swap(A, pos, ok);
        reverse(A, pos + 1, len - 1);


        return true;
    }

    //次の順列に書き換える、最小値ならfalseを返す
    public static boolean prevPermutation(int A[])
    {
        int len = A.length;
        int pos = len - 2;
        for (; pos >= 0; pos--)
        {
            if (A[pos] > A[pos + 1]) break;
        }
        if (pos == -1) return false;

        //posより小さい最大の数を二分探索
        int ok = pos + 1;
        int ng = len;
        while (Math.abs(ng - ok) > 1)
        {
            int mid = (ok + ng) / 2;
            if (A[mid] < A[pos]) ok = mid;
            else ng = mid;

        }

        swap(A, pos, ok);
        reverse(A, pos + 1, len - 1);


        return true;
    }

    //↓nCrをmod計算するために必要。　***factorial(N)を呼ぶ必要がある***
    static long ncr(int n, int r)
    {
        if (n < r) return 0;
        else if (r == 0) return 1;

        factorial(n);
        return F[n] / (F[n - r] * F[r]);
    }

    static long ncr2(int a, int b)
    {
        if (b == 0) return 1;
        else if (a < b) return 0;
        long res = 1;
        for (int i = 0; i < b; i++)
        {
            res *= a - i;
            res /= i + 1;
        }
        return res;
    }

    static long ncrdp(int n, int r)
    {
        if (n < r) return 0;
        long[][] dp = new long[n + 1][r + 1];
        for (int ni = 0; ni < n + 1; ni++)
        {
            dp[ni][0] = dp[ni][ni] = 1;
            for (int ri = 1; ri < ni; ri++)
            {
                dp[ni][ri] = dp[ni - 1][ri - 1] + dp[ni - 1][ri];
            }
        }
        return dp[n][r];
    }

    static long modNcr(int n, int r)
    {
        if (n < r) return 0;
        long result = F[n];
        result = result * modInv(F[n - r]) % MOD;
        result = result * modInv(F[r]) % MOD;
        return result;
    }

    public static long modSum(long... lar)
    {
        long res = 0;
        for (long l : lar)
            res = (res + l % MOD) % MOD;
        return res;
    }

    public static long modDiff(long a, long b)
    {
        long res = a - b;
        if (res < 0) res += MOD;
        res %= MOD;
        return res;
    }

    public static long modMul(long... lar)
    {
        long res = 1;
        for (long l : lar)
            res = (res * l) % MOD;
        if (res < 0) res += MOD;
        res %= MOD;
        return res;
    }

    public static long modDiv(long a, long b)
    {
        long x = a % MOD;
        long y = b % MOD;
        long res = (x * modInv(y)) % MOD;
        return res;
    }

    static long modInv(long n)
    {
        return modPow(n, MOD - 2);
    }

    static void factorial(int n)
    {
        F = new long[n + 1];
        F[0] = F[1] = 1;
//        for (int i = 2; i <= n; i++)
//        {
//            F[i] = (F[i - 1] * i) % MOD;
//        }
        //
        for (int i = 2; i <= 100000; i++)
        {
            F[i] = (F[i - 1] * i) % MOD;
        }
        for (int i = 100001; i <= n; i++)
        {
            F[i] = (F[i - 1] * i) % MOD;
        }
    }

    static long modPow(long x, long n)
    {
        long res = 1L;
        while (n > 0)
        {
            if ((n & 1) == 1)
            {
                res = res * x % MOD;
            }
            x = x * x % MOD;
            n >>= 1;
        }
        return res;
    }

    //↑nCrをmod計算するために必要

    static int gcd(int n, int r)
    {
        return r == 0 ? n : gcd(r, n % r);
    }

    static long gcd(long n, long r)
    {
        return r == 0 ? n : gcd(r, n % r);
    }

    static <T> void swap(T[] x, int i, int j)
    {
        T t = x[i];
        x[i] = x[j];
        x[j] = t;
    }

    static void swap(int[] x, int i, int j)
    {
        int t = x[i];
        x[i] = x[j];
        x[j] = t;
    }

    public static void reverse(int[] x)
    {
        int l = 0;
        int r = x.length - 1;
        while (l < r)
        {
            int temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }

    public static void reverse(long[] x)
    {
        int l = 0;
        int r = x.length - 1;
        while (l < r)
        {
            long temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }

    public static void reverse(int[] x, int s, int e)
    {
        int l = s;
        int r = e;
        while (l < r)
        {
            int temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }

    static int length(int a)
    {
        int cou = 0;
        while (a != 0)
        {
            a /= 10;
            cou++;
        }
        return cou;
    }

    static int length(long a)
    {
        int cou = 0;
        while (a != 0)
        {
            a /= 10;
            cou++;
        }
        return cou;
    }

    static int cou(boolean[] a)
    {
        int res = 0;
        for (boolean b : a)
        {
            if (b) res++;
        }
        return res;
    }

    static int countC2(char[][] a, char c)
    {
        int co = 0;
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                if (a[i][j] == c) co++;
        return co;
    }

    static int countI(int[] a, int key)
    {
        int co = 0;
        for (int i = 0; i < a.length; i++)
            if (a[i] == key) co++;
        return co;
    }

    static int countI(int[][] a, int key)
    {
        int co = 0;
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                if (a[i][j] == key) co++;
        return co;
    }

    static void fill(int[][] a, int v)
    {
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                a[i][j] = v;
    }


    static void fill(long[][] a, long v)
    {
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                a[i][j] = v;
    }

    static void fill(int[][][] a, int v)
    {
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                for (int k = 0; k < a[0][0].length; k++)
                    a[i][j][k] = v;
    }

    static int max(int... a)
    {
        int res = Integer.MIN_VALUE;
        for (int i : a)
        {
            res = Math.max(res, i);
        }
        return res;
    }


    static int max(int[][] ar)
    {
        int res = Integer.MIN_VALUE;
        for (int i[] : ar)
            res = Math.max(res, max(i));
        return res;
    }

    static int min(int... a)
    {
        int res = Integer.MAX_VALUE;
        for (int i : a)
        {
            res = Math.min(res, i);
        }
        return res;
    }


    static int min(int[][] ar)
    {
        int res = Integer.MAX_VALUE;
        for (int i[] : ar)
            res = Math.min(res, min(i));
        return res;
    }

    static int sum(int[] a)
    {
        int cou = 0;
        for (int i : a)
            cou += i;
        return cou;
    }

    static int abs(int a)
    {
        return Math.abs(a);
    }

    static class FastScanner
    {

        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public FastScanner(InputStream in)
        {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        public String next()
        {
            if (tokenizer == null || !tokenizer.hasMoreTokens())
            {
                try
                {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e)
                {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        /*public String nextChar(){
            return (char)next()[0];
        }*/
        public String nextLine()
        {
            if (tokenizer == null || !tokenizer.hasMoreTokens())
            {
                try
                {
                    return reader.readLine();
                } catch (IOException e)
                {
                    throw new RuntimeException(e);
                }
            }

            return tokenizer.nextToken("\n");
        }

        public long nextLong()
        {
            return Long.parseLong(next());
        }

        public int nextInt()
        {
            return Integer.parseInt(next());
        }

        public double nextDouble()
        {
            return Double.parseDouble(next());
        }

        public int[] nextIntArray(int n)
        {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = nextInt();
            }
            return a;
        }

        public int[] nextIntArrayDec(int n)
        {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = nextInt() - 1;
            }
            return a;
        }

        public int[][] nextIntArray2(int h, int w)
        {
            int[][] a = new int[h][w];
            for (int hi = 0; hi < h; hi++)
            {
                for (int wi = 0; wi < w; wi++)
                {
                    a[hi][wi] = nextInt();
                }
            }
            return a;
        }

        public int[][] nextIntArray2Dec(int h, int w)
        {
            int[][] a = new int[h][w];
            for (int hi = 0; hi < h; hi++)
            {
                for (int wi = 0; wi < w; wi++)
                {
                    a[hi][wi] = nextInt() - 1;
                }
            }
            return a;
        }

        //複数の配列を受け取る
        public void nextIntArrays2ar(int[] a, int[] b)
        {
            for (int i = 0; i < a.length; i++)
            {
                a[i] = sc.nextInt();
                b[i] = sc.nextInt();
            }
        }

        public void nextIntArrays2arDec(int[] a, int[] b)
        {
            for (int i = 0; i < a.length; i++)
            {
                a[i] = sc.nextInt() - 1;
                b[i] = sc.nextInt() - 1;
            }
        }

        //複数の配列を受け取る
        public void nextIntArrays3ar(int[] a, int[] b, int[] c)
        {
            for (int i = 0; i < a.length; i++)
            {
                a[i] = sc.nextInt();
                b[i] = sc.nextInt();
                c[i] = sc.nextInt();
            }
        }

        //複数の配列を受け取る
        public void nextIntArrays3arDecLeft2(int[] a, int[] b, int[] c)
        {
            for (int i = 0; i < a.length; i++)
            {
                a[i] = sc.nextInt() - 1;
                b[i] = sc.nextInt() - 1;
                c[i] = sc.nextInt();
            }
        }

        public Integer[] nextIntegerArray(int n)
        {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = nextInt();
            }
            return a;
        }

        public char[] nextCharArray(int n)
        {
            char[] a = next().toCharArray();

            return a;
        }

        public char[][] nextCharArray2(int h, int w)
        {
            char[][] a = new char[h][w];
            for (int i = 0; i < h; i++)
            {
                a[i] = next().toCharArray();
            }
            return a;
        }

        //スペースが入っている場合
        public char[][] nextCharArray2s(int h, int w)
        {
            char[][] a = new char[h][w];
            for (int i = 0; i < h; i++)
            {
                a[i] = nextLine().replace(" ", "").toCharArray();
            }
            return a;
        }

        public char[][] nextWrapCharArray2(int h, int w, char c)
        {
            char[][] a = new char[h + 2][w + 2];
            //char c = '*';
            int i;
            for (i = 0; i < w + 2; i++)
                a[0][i] = c;
            for (i = 1; i < h + 1; i++)
            {
                a[i] = (c + next() + c).toCharArray();
            }
            for (i = 0; i < w + 2; i++)
                a[h + 1][i] = c;
            return a;
        }

        //スペースが入ってる時用
        public char[][] nextWrapCharArray2s(int h, int w, char c)
        {
            char[][] a = new char[h + 2][w + 2];
            //char c = '*';
            int i;
            for (i = 0; i < w + 2; i++)
                a[0][i] = c;
            for (i = 1; i < h + 1; i++)
            {
                a[i] = (c + nextLine().replace(" ", "") + c).toCharArray();
            }
            for (i = 0; i < w + 2; i++)
                a[h + 1][i] = c;
            return a;
        }

        public long[] nextLongArray(int n)
        {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = nextLong();
            }
            return a;
        }

        public long[][] nextLongArray2(int h, int w)
        {
            long[][] a = new long[h][w];
            for (int hi = 0; hi < h; hi++)
            {
                for (int wi = 0; wi < w; wi++)
                {
                    a[hi][wi] = nextLong();
                }
            }
            return a;
        }
    }
}