Problem: 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.

Examples

Input

3 7
2 0
3 2
0 3


Output

2


Input

1 3
0 3


Output

0


Input

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


Output

5


Input

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


Output

3

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.Map;
import java.io.OutputStreamWriter;
import java.io.OutputStream;
import java.io.IOException;
import java.io.UncheckedIOException;
import java.util.List;
import java.util.TreeMap;
import java.io.Closeable;
import java.util.Map.Entry;
import java.io.Writer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            DMangaMarket solver = new DMangaMarket();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class DMangaMarket {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            long t = in.readInt();
            List<Store> nonZero = new ArrayList<>(n);
            List<Store> zero = new ArrayList<>(n);

            for (int i = 0; i < n; i++) {
                int a = in.readInt();
                int b = in.readInt();
                Store store = new Store();
                store.a = a;
                store.b = b;
                if (a == 0) {
                    zero.add(store);
                } else {
                    nonZero.add(store);
                }
            }

            zero.sort((a, b) -> Long.compare(a.b, b.b));
            nonZero.sort((a, b) -> Long.compare((a.b + 1) * b.a, (b.b + 1) * a.a));
            int m = nonZero.size();
            long[][] dp = new long[m + 1][30];
            long inf = (long) 1e18;
            SequenceUtils.deepFill(dp, inf);
            dp[0][0] = 0;
            for (int i = 1; i <= m; i++) {
                Store s = nonZero.get(i - 1);
                for (int j = 0; j < 30; j++) {
                    dp[i][j] = dp[i - 1][j];
                    if (j > 0) {
                        dp[i][j] = Math.min(dp[i][j], dp[i - 1][j - 1] + 1 + DigitUtils.mul(dp[i - 1][j - 1] + 1, s.a, inf, inf) + s.b);
                    }
                }
            }

            long sum = 0;
            TreeMap<Long, Integer> map = new TreeMap<>();
            for (int i = 0; i < zero.size(); i++) {
                Store s = zero.get(i);
                sum += s.b + 1;
                map.put(sum, i + 1);
            }

            long ans = 0;
            for (int i = 0; i < 30; i++) {
                if (dp[m][i] > t) {
                    continue;
                }
                Map.Entry<Long, Integer> floor = map.floorEntry(t - dp[m][i]);
                ans = Math.max(ans, i + (floor == null ? 0 : floor.getValue()));
            }

            out.println(ans);
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 20];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class DigitUtils {
        private DigitUtils() {
        }

        public static boolean isMultiplicationOverflow(long a, long b, long limit) {
            if (limit < 0) {
                limit = -limit;
            }
            if (a < 0) {
                a = -a;
            }
            if (b < 0) {
                b = -b;
            }
            if (a == 0 || b == 0) {
                return false;
            }
            //a * b > limit => a > limit / b
            return a > limit / b;
        }

        public static long mul(long a, long b, long limit, long overflowVal) {
            return isMultiplicationOverflow(a, b, limit) ? overflowVal : a * b;
        }

    }

    static class Store {
        long a;
        long b;

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput append(long c) {
            cache.append(c);
            return this;
        }

        public FastOutput println(long c) {
            return append(c).println();
        }

        public FastOutput println() {
            cache.append(System.lineSeparator());
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static class SequenceUtils {
        public static void deepFill(Object array, long val) {
            if (!array.getClass().isArray()) {
                throw new IllegalArgumentException();
            }
            if (array instanceof long[]) {
                long[] longArray = (long[]) array;
                Arrays.fill(longArray, val);
            } else {
                Object[] objArray = (Object[]) array;
                for (Object obj : objArray) {
                    deepFill(obj, val);
                }
            }
        }

    }
}