Problem:
Score : 800 points

Problem Statement

There are N stores called Store 1, Store 2, \cdots, Store N. Takahashi, who is at his house at time 0, is planning to visit some of these stores.

It takes Takahashi one unit of time to travel from his house to one of the stores, or between any two stores.

If Takahashi reaches Store i at time t, he can do shopping there after standing in a queue for a_i \times t + b_i units of time. (We assume that it takes no time other than waiting.)

All the stores close at time T + 0.5. If Takahashi is standing in a queue for some store then, he cannot do shopping there.

Takahashi does not do shopping more than once in the same store.

Find the maximum number of times he can do shopping before time T + 0.5.

Constraints

All values in input are integers.

1 \leq N \leq 2 \times 10^5

0 \leq a_i \leq 10^9

0 \leq b_i \leq 10^9

0 \leq T \leq 10^9

Input

Input is given from Standard Input in the following format:

N T
a_1 b_1
a_2 b_2
\vdots
a_N b_N

Output

Print the answer.

Sample Input 1

3 7
2 0
3 2
0 3

Sample Output 1

2

Here is one possible way to visit stores:

From time 0 to time 1: in 1 unit of time, he travels from his house to Store 1.

From time 1 to time 3: for 2 units of time, he stands in a queue for Store 1 to do shopping.

From time 3 to time 4: in 1 unit of time, he travels from Store 1 to Store 3.

From time 4 to time 7: for 3 units of time, he stands in a queue for Store 3 to do shopping.

In this way, he can do shopping twice before time 7.5.

Sample Input 2

1 3
0 3

Sample Output 2

0

Sample Input 3

5 21600
2 14
3 22
1 3
1 10
1 9

Sample Output 3

5

Sample Input 4

7 57
0 25
3 10
2 4
5 15
3 22
2 14
1 15

Sample Output 4

3

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.util.Arrays;

public class Main {

  private static void solve() {
    int n = ni();

    long t = nl();
    long[][] p = new long[n][2];
    for (int i = 0; i < n; i++) {
      p[i][0] = nl();
      p[i][1] = nl();
    }

    Arrays.sort(p, (o1, o2) -> {
      long x = o2[0] * (o1[1] + 1) - o1[0] * (o2[1] + 1);
      if (x != 0) {
        return Long.signum(x);
      } else {
        return Long.signum(o1[0] == o2[0] ? o1[1] - o2[1] : o1[0] - o2[0]);
      }
    });

    long inf = Integer.MAX_VALUE;
    int m = 28;
    long[][] dp = new long[n + 1][m];
    for (long[] v : dp)
      Arrays.fill(v, inf);
    dp[0][0] = 0;



    for (int i = 1; i <= n; i++) {
      long[] q = p[i - 1];
      long a = q[0] + 1;
      long b = q[0] + q[1] + 1;

      dp[i][0] = 0;
      for (int j = 1; j <= Math.min(i, m); j++) {
        if (q[0] == 0) {
          dp[i][j] = dp[i - 1][j];
        } else {
          long nex = dp[i - 1][j - 1] >= inf ? inf : a * dp[i - 1][j - 1] + b;
          dp[i][j] = Math.min(dp[i - 1][j], Math.min(nex, inf));
        }
      }
    }

    int ret = 0;
    for (int i = 0; i <= m; i++) {
      if (dp[n][i] > t)
        break;

      int now = i;
      long nt = dp[n][i];
      for (int j = 0; j < n; j++) {
        if (p[j][0] != 0) {
          continue;
        }

        if (nt + p[j][1] + 1 <= t) {
          nt += p[j][1] + 1;
          now++;
        } else {
          break;
        }
      }
      ret = Math.max(now, ret);
    }

    System.out.println(ret);
  }

  class SegmentTreeRMQ {
    public int M, H, N;
    public int[] st;

    public SegmentTreeRMQ(int n) {
      N = n;
      M = Integer.highestOneBit(Math.max(N - 1, 1)) << 2;
      H = M >>> 1;
      st = new int[M];
      Arrays.fill(st, 0, M, Integer.MAX_VALUE);
    }

    public SegmentTreeRMQ(int[] a) {
      N = a.length;
      M = Integer.highestOneBit(Math.max(N - 1, 1)) << 2;
      H = M >>> 1;
      st = new int[M];
      for (int i = 0; i < N; i++) {
        st[H + i] = a[i];
      }
      Arrays.fill(st, H + N, M, Integer.MAX_VALUE);
      for (int i = H - 1; i >= 1; i--)
        propagate(i);
    }

    public void update(int pos, int x) {
      st[H + pos] = x;
      for (int i = (H + pos) >>> 1; i >= 1; i >>>= 1)
        propagate(i);
    }

    private void propagate(int i) {
      st[i] = Math.min(st[2 * i], st[2 * i + 1]);
    }

    public int minx(int l, int r) {
      int min = Integer.MAX_VALUE;
      if (l >= r)
        return min;
      while (l != 0) {
        int f = l & -l;
        if (l + f > r)
          break;
        int v = st[(H + l) / f];
        if (v < min)
          min = v;
        l += f;
      }

      while (l < r) {
        int f = r & -r;
        int v = st[(H + r) / f - 1];
        if (v < min)
          min = v;
        r -= f;
      }
      return min;
    }

    public int min(int l, int r) {
      return l >= r ? 0 : min(l, r, 0, H, 1);
    }

    private int min(int l, int r, int cl, int cr, int cur) {
      if (l <= cl && cr <= r) {
        return st[cur];
      } else {
        int mid = cl + cr >>> 1;
        int ret = Integer.MAX_VALUE;
        if (cl < r && l < mid) {
          ret = Math.min(ret, min(l, r, cl, mid, 2 * cur));
        }
        if (mid < r && l < cr) {
          ret = Math.min(ret, min(l, r, mid, cr, 2 * cur + 1));
        }
        return ret;
      }
    }

    public int firstle(int l, int v) {
      int cur = H + l;
      while (true) {
        if (st[cur] <= v) {
          if (cur < H) {
            cur = 2 * cur;
          } else {
            return cur - H;
          }
        } else {
          cur++;
          if ((cur & cur - 1) == 0)
            return -1;
          if ((cur & 1) == 0)
            cur >>>= 1;
        }
      }
    }

    public int lastle(int l, int v) {
      int cur = H + l;
      while (true) {
        if (st[cur] <= v) {
          if (cur < H) {
            cur = 2 * cur + 1;
          } else {
            return cur - H;
          }
        } else {
          if ((cur & cur - 1) == 0)
            return -1;
          cur--;
          if ((cur & 1) == 1)
            cur >>>= 1;
        }
      }
    }
  }


  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}