You are given n non-decreasing arrays of non-negative numbers. 

Vasya repeats the following operation k times: 

  * Selects a non-empty array. 
  * Puts the first element of the selected array in his pocket. 
  * Removes the first element from the selected array. 



Vasya wants to maximize the sum of the elements in his pocket.

Input

The first line contains two integers n and k (1 ≤ n, k ≤ 3 000): the number of arrays and operations.

Each of the next n lines contain an array. The first integer in each line is t_i (1 ≤ t_i ≤ 10^6): the size of the i-th array. The following t_i integers a_{i, j} (0 ≤ a_{i, 1} ≤ … ≤ a_{i, t_i} ≤ 10^8) are the elements of the i-th array.

It is guaranteed that k ≤ ∑_{i=1}^n t_i ≤ 10^6.

Output

Print one integer: the maximum possible sum of all elements in Vasya's pocket after k operations.

Example

Input


3 3
2 5 10
3 1 2 3
2 1 20


Output


26
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.Arrays;
import java.util.Collection;
import java.io.IOException;
import java.util.Deque;
import java.util.function.Supplier;
import java.io.UncheckedIOException;
import java.util.function.Consumer;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.ArrayDeque;
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 << 29);
        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);
            DSum solver = new DSum();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class DSum {
        long inf = (long) 1e18;
        int k;
        Buffer<long[]> buffer = new Buffer<>(() -> {
            long[] ans = new long[k + 1];
            Arrays.fill(ans, -inf);
            return ans;
        }, x -> {
            Arrays.fill(x, -inf);
        });
        long[][] ps;
        long best = 0;

        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            k = in.readInt();
            ps = new long[n][];
            for (int i = 0; i < n; i++) {
                int t = in.readInt();
                ps[i] = new long[t + 1];
                for (int j = 1; j <= t; j++) {
                    ps[i][j] = in.readInt();
                    ps[i][j] += ps[i][j - 1];
                }
            }

            long[] dp = buffer.alloc();
            dp[0] = 0;

            dac(dp, 0, n - 1);
            out.println(best);
        }

        public long[] solve(int l, int r, long[] cur) {
            long[] prev = buffer.alloc();
            System.arraycopy(cur, 0, prev, 0, k);
            for (int i = l; i <= r; i++) {
                int w = ps[i].length - 1;
                long v = ps[i][w];
                for (int j = k; j >= w; j--) {
                    prev[j] = Math.max(prev[j], prev[j - w] + v);
                }
            }
            return prev;
        }

        public void dac(long[] cur, int l, int r) {
            if (l == r) {
                for (int j = 0; j < ps[l].length && j <= k; j++) {
                    best = Math.max(best, ps[l][j] + cur[k - j]);
                }
                return;
            }
            int m = DigitUtils.floorAverage(l, r);
            long[] left = solve(l, m, cur);
            dac(left, m + 1, r);
            buffer.release(left);

            long[] right = solve(m + 1, r, cur);
            dac(right, l, m);
            buffer.release(right);
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private static final int THRESHOLD = 1 << 13;
        private final Writer os;
        private StringBuilder cache = new StringBuilder(THRESHOLD * 2);

        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;
        }

        private void afterWrite() {
            if (cache.length() < THRESHOLD) {
                return;
            }
            flush();
        }

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

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

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

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

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

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

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

        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 Buffer<T> {
        private Deque<T> deque;
        private Supplier<T> supplier;
        private Consumer<T> cleaner;
        private int allocTime;
        private int releaseTime;

        public Buffer(Supplier<T> supplier) {
            this(supplier, (x) -> {
            });
        }

        public Buffer(Supplier<T> supplier, Consumer<T> cleaner) {
            this(supplier, cleaner, 0);
        }

        public Buffer(Supplier<T> supplier, Consumer<T> cleaner, int exp) {
            this.supplier = supplier;
            this.cleaner = cleaner;
            deque = new ArrayDeque<>(exp);
        }

        public T alloc() {
            allocTime++;
            return deque.isEmpty() ? supplier.get() : deque.removeFirst();
        }

        public void release(T e) {
            releaseTime++;
            cleaner.accept(e);
            deque.addLast(e);
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        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 int floorAverage(int x, int y) {
            return (x & y) + ((x ^ y) >> 1);
        }

    }
}

