Problem:
Score : 1000 points

Problem Statement

Rng is baking cookies.

Initially, he can bake one cookie per second.

He can also eat the cookies baked by himself.
When there are x cookies not yet eaten, he can choose to eat all those cookies. After he finishes eating those cookies, the number of cookies he can bake per second becomes x. Note that a cookie always needs to be baked for 1 second, that is, he cannot bake a cookie in 1/x seconds when x > 1.
When he choose to eat the cookies, he must eat all of them; he cannot choose to eat only part of them.
It takes him A seconds to eat the cookies regardless of how many, during which no cookies can be baked.

He wants to give N cookies to Grandma.
Find the shortest time needed to produce at least N cookies not yet eaten.

Constraints

1≦N≦10^{12}

0≦A≦10^{12}

A is an integer.

Partial Score

500 points will be awarded for passing the test set satisfying N≦10^6 and A≦10^6.

Additional 500 points will be awarded for passing the test set without additional constraints.

Input

The input is given from Standard Input in the following format:

N A

Output

Print the shortest time needed to produce at least N cookies not yet eaten.

Sample Input 1

8 1

Sample Output 1

7

It is possible to produce 8 cookies in 7 seconds, as follows:

After 1 second: 1 cookie is done.

After 2 seconds: 1 more cookie is done, totaling 2. Now, Rng starts eating those 2 cookies.

After 3 seconds: He finishes eating the cookies, and he can now bake 2 cookies per second.

After 4 seconds: 2 cookies are done.

After 5 seconds: 2 more cookies are done, totaling 4.

After 6 seconds: 2 more cookies are done, totaling 6.

After 7 seconds: 2 more cookies are done, totaling 8.

Sample Input 2

1000000000000 1000000000000

Sample Output 2

1000000000000

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.NoSuchElementException;

/*
                   _ooOoo_
                  o8888888o
                  88" . "88
                  (| -_- |)
                  O\  =  /O
               ____/`---'\____
             .'  \\|     |//  `.
            /  \\|||  :  |||//  \
           /  _||||| -:- |||||-  \
           |   | \\\  -  /// |   |
           | \_|  ''\---/''  |   |
           \  .-\__  `-`  ___/-. /
         ___`. .'  /--.--\  `. . __
      ."" '<  `.___\_<|>_/___.'  >'"".
     | | :  `- \`.;`\ _ /`;.`/ - ` : | |
     \  \ `-.   \_ __\ /__ _/   .-` /  /
======`-.____`-.___\_____/___.-`____.-'======
                   `=---='
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
            pass System Test!
*/

public class Main {
  private static class Task {
    long N, A;

    long pow(long x, long e) {
      long ret = 1;
      long cur = x;
      while (e > 0) {
        if ((e & 1) != 0) {
          ret = (ret * cur);
        }
        cur = (cur * cur);
        e /= 2;
      }
      return ret;
    }

    void solve(FastScanner in, PrintWriter out) throws Exception {
      N = in.nextLong();
      A = in.nextLong();

      BigInteger min = BigInteger.valueOf(N);
      BigInteger n = BigInteger.valueOf(N);
      BigInteger a = BigInteger.valueOf(A);
      for (long X = 2; X < 1000000; X++) {
        for (int K = 0; K < 70; K++) {
          BigInteger x = BigInteger.valueOf(X);
          BigInteger k = BigInteger.valueOf(K);
          BigInteger t = (x.add(a)).multiply(k);
          if (t.compareTo(min) > 0) continue;
          BigInteger xk = x.pow(K);
          xk = xk.min(n);
          BigInteger s = (n.add(xk).subtract(BigInteger.ONE)).divide(xk);

          BigInteger ans = t.add(s);
          min = ans.min(min);
        }
      }
      out.println(min.longValue());
    }

    class UnionFind {
      // par[i]：データiが属する木の親の番号。i == par[i]のとき、データiは木の根ノードである
      private int[] par;
      // sizes[i]：根ノードiの木に含まれるデータの数。iが根ノードでない場合は無意味な値となる
      private int[] sizes;

      // 木の数
      private int size;

      UnionFind(int n) {
        par = new int[n];
        sizes = new int[n];
        size = n;
        Arrays.fill(sizes, 1);
        // 最初は全てのデータiがグループiに存在するものとして初期化
        for (int i = 0; i < n; i++) par[i] = i;
      }

      /**
       * データxが属する木の根を得る
       *
       * @param x
       * @return
       */
      int find(int x) {
        if (x == par[x]) return x;
        return par[x] = find(par[x]);  // 根を張り替えながら再帰的に根ノードを探す
      }

      /**
       * 2つのデータx, yが属する木をマージする。
       * マージが必要なら true を返す
       *
       * @param x
       * @param y
       * @return
       */
      boolean unite(int x, int y) {
        // データの根ノードを得る
        x = find(x);
        y = find(y);

        // 既に同じ木に属しているならマージしない
        if (x == y) return false;

        // xの木がyの木より大きくなるようにする
        if (sizes[x] < sizes[y]) {
          int tx = x;
          x = y;
          y = tx;
        }

        // xがyの親になるように連結する
        par[y] = x;
        sizes[x] += sizes[y];
        sizes[y] = 0;  // sizes[y]は無意味な値となるので0を入れておいてもよい

        size--;
        return true;
      }

      /**
       * 2つのデータx, yが属する木が同じならtrueを返す
       *
       * @param x
       * @param y
       * @return
       */
      boolean isSame(int x, int y) {
        return find(x) == find(y);
      }

      /**
       * データxが含まれる木の大きさを返す
       *
       * @param x
       * @return
       */
      int partialSizeOf(int x) {
        return sizes[find(x)];
      }

      /**
       * 木の数を返す
       *
       * @return
       */
      int size() {
        return size;
      }
    }
  }

  /**
   * ここから下はテンプレートです。
   */
  public static void main(String[] args) throws Exception {
    OutputStream outputStream = System.out;
    FastScanner in = new FastScanner();
    PrintWriter out = new PrintWriter(outputStream);
    Task solver = new Task();
    solver.solve(in, out);
    out.close();
  }
  private static class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int bufferLength = 0;

    private boolean hasNextByte() {
      if (ptr < bufferLength) {
        return true;
      } else {
        ptr = 0;
        try {
          bufferLength = in.read(buffer);
        } catch (IOException e) {
          e.printStackTrace();
        }
        if (bufferLength <= 0) {
          return false;
        }
      }
      return true;
    }

    private int readByte() {
      if (hasNextByte()) return buffer[ptr++];
      else return -1;
    }

    private static boolean isPrintableChar(int c) {
      return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
    }

    boolean hasNext() {
      skipUnprintable();
      return hasNextByte();
    }

    public String next() {
      if (!hasNext()) throw new NoSuchElementException();
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while (isPrintableChar(b)) {
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb.toString();
    }

    long nextLong() {
      if (!hasNext()) throw new NoSuchElementException();
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if (b == '-') {
        minus = true;
        b = readByte();
      }
      if (b < '0' || '9' < b) {
        throw new NumberFormatException();
      }
      while (true) {
        if ('0' <= b && b <= '9') {
          n *= 10;
          n += b - '0';
        } else if (b == -1 || !isPrintableChar(b)) {
          return minus ? -n : n;
        } else {
          throw new NumberFormatException();
        }
        b = readByte();
      }
    }

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

    double[] nextDoubleArray(int n) {
      double[] array = new double[n];
      for (int i = 0; i < n; i++) {
        array[i] = nextDouble();
      }
      return array;
    }

    double[][] nextDoubleMap(int n, int m) {
      double[][] map = new double[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextDoubleArray(m);
      }
      return map;
    }

    public int nextInt() {
      return (int) nextLong();
    }

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

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

    public String[] nextStringArray(int n) {
      String[] array = new String[n];
      for (int i = 0; i < n; i++) array[i] = next();
      return array;
    }

    public char[][] nextCharMap(int n) {
      char[][] array = new char[n][];
      for (int i = 0; i < n; i++) array[i] = next().toCharArray();
      return array;
    }

    public int[][] nextIntMap(int n, int m) {
      int[][] map = new int[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextIntArray(m);
      }
      return map;
    }
  }
}