Problem: You are given a circular array with n elements. The elements are numbered from some element with values from 1 to n in clockwise order. The i-th cell contains the value ai. The robot Simba is in cell s.

Each moment of time the robot is in some of the n cells (at the begin he is in s). In one turn the robot can write out the number written in current cell or move to the adjacent cell in clockwise or counterclockwise direction. To write out the number from the cell Simba doesn't spend any time, but to move to adjacent cell Simba spends one unit of time.

Simba wants to write the number from each cell one time, so the numbers will be written in a non decreasing order. Find the least number of time units to write out all numbers.

Input

The first line contains two integers n and s (1 ≤ s ≤ n ≤ 2000) — the number of cells in the circular array and the starting position of Simba.

The second line contains n integers ai ( - 109 ≤ ai ≤ 109) — the number written in the i-th cell. The numbers are given for cells in order from 1 to n. Some of numbers ai can be equal.

Output

In the first line print the number t — the least number of time units.

Each of the next n lines should contain the direction of robot movement and the number of cells to move in that direction. After that movement the robot writes out the number from the cell in which it turns out. The direction and the number of cells should be printed in the form of +x in case of clockwise movement and -x in case of counterclockwise movement to x cells (0 ≤ x ≤ n - 1).

Note that the sum of absolute values of x should be equal to t.

Examples

Input

9 1
0 1 2 2 2 1 0 1 1


Output

12
+0
-3
-1
+2
+1
+2
+1
+1
+1


Input

8 1
0 1 0 1 0 1 0 1


Output

13
+0
+2
+2
+2
-1
+2
+2
+2


Input

8 1
1 2 3 4 5 6 7 8


Output

7
+0
+1
+1
+1
+1
+1
+1
+1


Input

8 1
0 0 0 0 0 0 0 0


Output

7
+0
+1
+1
+1
+1
+1
+1
+1

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Iterator;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.NoSuchElementException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Egor Kulikov (egor@egork.net)
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskF solver = new TaskF();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskF {
		public void solve(int testNumber, InputReader in, OutputWriter out) {
			int n = in.readInt();
			int s = in.readInt() - 1;
			int[] a = IOUtils.readIntArray(in, n);
			ArrayUtils.compress(a);
			int[] first = ArrayUtils.createArray(ArrayUtils.maxElement(a) + 1, -1);
			int[] next = new int[n];
			int[] toLeft = ArrayUtils.createArray(n, -1);
			int[] toRight = ArrayUtils.createArray(n, -1);
			int[] last = new int[first.length];
			for (int i = 0; i < n; i++) {
				next[i] = first[a[i]];
				first[a[i]] = i;
				if (next[i] == -1) {
					last[a[i]] = i;
				} else {
					toLeft[i] = next[i];
					toRight[next[i]] = i;
				}
			}
			for (int i = 0; i < first.length; i++) {
				if (first[i] != last[i]) {
					toRight[first[i]] = last[i];
					toLeft[last[i]] = first[i];
				}
			}
			int[] answer = new int[n];
			IntList[] prev = new IntList[n];
			for (int i = first[0]; i != -1; i = next[i]) {
				if (toLeft[i] == -1) {
					prev[i] = new IntArrayList();
					prev[i].add(i);
					answer[i] = dst(s, i, n);
				} else {
					int distance = toLeft[i] - i;
					if (distance < 0) {
						distance += n;
					}
					distance += dst(s, toLeft[i], n);
					int other = i - toRight[i];
					if (other < 0) {
						other += n;
					}
					other += dst(s, toRight[i], n);
					prev[i] = new IntArrayList();
					if (distance < other) {
						int pos = toLeft[i];
						while (pos != i) {
							if (a[pos] == 0) {
								prev[i].add(pos);
							}
							pos--;
							if (pos < 0) {
								pos += n;
							}
						}
						prev[i].add(i);
					} else {
						int pos = toRight[i];
						while (pos != i) {
							if (a[pos] == 0) {
								prev[i].add(pos);
							}
							pos++;
							if (pos >= n) {
								pos -= n;
							}
						}
						prev[i].add(i);
					}
					answer[i] = Math.min(distance, other);
				}
			}
			for (int i = 1; i < first.length; i++) {
				for (int j = first[i]; j != -1; j = next[j]) {
					int bestAt = -1;
					int best = Integer.MAX_VALUE;
					boolean dir = false;
					for (int k = first[i - 1]; k != -1; k = next[k]) {
						if (toLeft[j] == -1) {
							int candidate = Math.abs(k - j);
							candidate = Math.min(candidate, n - candidate);
							candidate += answer[k];
							if (candidate < best) {
								best = candidate;
								bestAt = k;
							}
						} else {
							int left = Math.abs(toLeft[j] - k);
							left = Math.min(left, n - left);
							left += answer[k];
							left += toLeft[j] - j < 0 ? toLeft[j] - j + n : toLeft[j] - j;
							if (left < best) {
								best = left;
								bestAt = k;
								dir = true;
							}
							int right = Math.abs(toRight[j] - k);
							right = Math.min(right, n - right);
							right += answer[k];
							right += j - toRight[j] < 0 ? j - toRight[j] + n : j - toRight[j];
							if (right < best) {
								best = right;
								bestAt = k;
								dir = false;
							}
						}
					}
					answer[j] = best;
					prev[j] = new IntArrayList(prev[bestAt]);
					if (toLeft[j] != -1) {
						if (dir) {
							int pos = toLeft[j];
							while (pos != j) {
								if (a[pos] == i) {
									prev[j].add(pos);
								}
								pos--;
								if (pos < 0) {
									pos += n;
								}
							}
							prev[j].add(j);
						} else {
							int pos = toRight[j];
							while (pos != j) {
								if (a[pos] == i) {
									prev[j].add(pos);
								}
								pos++;
								if (pos >= n) {
									pos -= n;
								}
							}
							prev[j].add(j);
						}
					} else {
						prev[j].add(j);
					}
				}
			}
			int best = Integer.MAX_VALUE;
			int bestAt = -1;
			for (int i = first[first.length - 1]; i != -1; i = next[i]) {
				if (answer[i] < best) {
					best = answer[i];
					bestAt = i;
				}
			}
			out.printLine(best);
			int at = s;
			for (int i : prev[bestAt]) {
				int left = at - i;
				if (left < 0) {
					left += n;
				}
				int right = i - at;
				if (right < 0) {
					right += n;
				}
				if (right <= left) {
					out.print('+');
					out.printLine(right);
				} else {
					out.print('-');
					out.printLine(left);
				}
				at = i;
			}
		}

		private int dst(int f, int i, int n) {
			return Math.min(Math.abs(f - i), n - Math.abs(f - i));
		}

	}

	static class IntArray extends IntAbstractStream implements IntList {
		private int[] data;

		public IntArray(int[] arr) {
			data = arr;
		}

		public int size() {
			return data.length;
		}

		public int get(int at) {
			return data[at];
		}

		public void addAt(int index, int value) {
			throw new UnsupportedOperationException();
		}

		public void removeAt(int index) {
			throw new UnsupportedOperationException();
		}

		public void set(int index, int value) {
			data[index] = value;
		}

	}

	static class IOUtils {
		public static int[] readIntArray(InputReader in, int size) {
			int[] array = new int[size];
			for (int i = 0; i < size; i++)
				array[i] = in.readInt();
			return array;
		}

	}

	static interface IntIterator {
		public int value() throws NoSuchElementException;

		public boolean advance();

		public boolean isValid();

	}

	static class ArrayUtils {
		public static int[] sort(int[] array, IntComparator comparator) {
			return sort(array, 0, array.length, comparator);
		}

		public static int[] sort(int[] array, int from, int to, IntComparator comparator) {
			if (from == 0 && to == array.length)
				new IntArray(array).sort(comparator);
			else
				new IntArray(array).subList(from, to).sort(comparator);
			return array;
		}

		public static int[] unique(int[] array) {
			return new IntArray(array).unique().toArray();
		}

		public static int maxElement(int[] array) {
			return new IntArray(array).max();
		}

		public static int[] compress(int[]... arrays) {
			int totalLength = 0;
			for (int[] array : arrays)
				totalLength += array.length;
			int[] all = new int[totalLength];
			int delta = 0;
			for (int[] array : arrays) {
				System.arraycopy(array, 0, all, delta, array.length);
				delta += array.length;
			}
			sort(all, IntComparator.DEFAULT);
			all = unique(all);
			for (int[] array : arrays) {
				for (int i = 0; i < array.length; i++)
					array[i] = Arrays.binarySearch(all, array[i]);
			}
			return all;
		}

		public static int[] createArray(int count, int value) {
			int[] array = new int[count];
			Arrays.fill(array, value);
			return array;
		}

	}

	static interface IntStream extends Iterable<Integer>, Comparable<IntStream> {
		public IntIterator intIterator();

		default public Iterator<Integer> iterator() {
			return new Iterator<Integer>() {
				private IntIterator it = intIterator();

				public boolean hasNext() {
					return it.isValid();
				}

				public Integer next() {
					int result = it.value();
					it.advance();
					return result;
				}
			};
		}

		default public int compareTo(IntStream c) {
			IntIterator it = intIterator();
			IntIterator jt = c.intIterator();
			while (it.isValid() && jt.isValid()) {
				int i = it.value();
				int j = jt.value();
				if (i < j) {
					return -1;
				} else if (i > j) {
					return 1;
				}
				it.advance();
				jt.advance();
			}
			if (it.isValid()) {
				return 1;
			}
			if (jt.isValid()) {
				return -1;
			}
			return 0;
		}

		default public int max() {
			int result = Integer.MIN_VALUE;
			for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
				int current = it.value();
				if (current > result) {
					result = current;
				}
			}
			return result;
		}

	}

	static interface IntReversableCollection extends IntCollection {
	}

	static interface IntCollection extends IntStream {
		public int size();

		default public void add(int value) {
			throw new UnsupportedOperationException();
		}

		default public int[] toArray() {
			int size = size();
			int[] array = new int[size];
			int i = 0;
			for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
				array[i++] = it.value();
			}
			return array;
		}

		default public IntCollection addAll(IntStream values) {
			for (IntIterator it = values.intIterator(); it.isValid(); it.advance()) {
				add(it.value());
			}
			return this;
		}

	}

	static class InputReader {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int readInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return isWhitespace(c);
		}

		public static boolean isWhitespace(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);

		}

	}

	static abstract class IntAbstractStream implements IntStream {

		public String toString() {
			StringBuilder builder = new StringBuilder();
			boolean first = true;
			for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
				if (first) {
					first = false;
				} else {
					builder.append(' ');
				}
				builder.append(it.value());
			}
			return builder.toString();
		}


		public boolean equals(Object o) {
			if (!(o instanceof IntStream)) {
				return false;
			}
			IntStream c = (IntStream) o;
			IntIterator it = intIterator();
			IntIterator jt = c.intIterator();
			while (it.isValid() && jt.isValid()) {
				if (it.value() != jt.value()) {
					return false;
				}
				it.advance();
				jt.advance();
			}
			return !it.isValid() && !jt.isValid();
		}


		public int hashCode() {
			int result = 0;
			for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
				result *= 31;
				result += it.value();
			}
			return result;
		}

	}

	static interface IntList extends IntReversableCollection {
		public abstract int get(int index);

		public abstract void set(int index, int value);

		public abstract void addAt(int index, int value);

		public abstract void removeAt(int index);

		default public void swap(int first, int second) {
			if (first == second) {
				return;
			}
			int temp = get(first);
			set(first, get(second));
			set(second, temp);
		}

		default public IntIterator intIterator() {
			return new IntIterator() {
				private int at;
				private boolean removed;

				public int value() {
					if (removed) {
						throw new IllegalStateException();
					}
					return get(at);
				}

				public boolean advance() {
					at++;
					removed = false;
					return isValid();
				}

				public boolean isValid() {
					return !removed && at < size();
				}

				public void remove() {
					removeAt(at);
					at--;
					removed = true;
				}
			};
		}


		default public void add(int value) {
			addAt(size(), value);
		}

		default public IntList sort(IntComparator comparator) {
			Sorter.sort(this, comparator);
			return this;
		}

		default IntList unique() {
			int last = Integer.MIN_VALUE;
			IntList result = new IntArrayList();
			int size = size();
			for (int i = 0; i < size; i++) {
				int current = get(i);
				if (current != last) {
					result.add(current);
					last = current;
				}
			}
			return result;
		}

		default public IntList subList(final int from, final int to) {
			return new IntList() {
				private final int shift;
				private final int size;

				{
					if (from < 0 || from > to || to > IntList.this.size()) {
						throw new IndexOutOfBoundsException("from = " + from + ", to = " + to + ", size = " + size());
					}
					shift = from;
					size = to - from;
				}

				public int size() {
					return size;
				}

				public int get(int at) {
					if (at < 0 || at >= size) {
						throw new IndexOutOfBoundsException("at = " + at + ", size = " + size());
					}
					return IntList.this.get(at + shift);
				}

				public void addAt(int index, int value) {
					throw new UnsupportedOperationException();
				}

				public void removeAt(int index) {
					throw new UnsupportedOperationException();
				}

				public void set(int at, int value) {
					if (at < 0 || at >= size) {
						throw new IndexOutOfBoundsException("at = " + at + ", size = " + size());
					}
					IntList.this.set(at + shift, value);
				}

				public IntList compute() {
					return new IntArrayList(this);
				}
			};
		}

	}

	static class IntArrayList extends IntAbstractStream implements IntList {
		private int size;
		private int[] data;

		public IntArrayList() {
			this(3);
		}

		public IntArrayList(int capacity) {
			data = new int[capacity];
		}

		public IntArrayList(IntCollection c) {
			this(c.size());
			addAll(c);
		}

		public IntArrayList(IntStream c) {
			this();
			if (c instanceof IntCollection) {
				ensureCapacity(((IntCollection) c).size());
			}
			addAll(c);
		}

		public IntArrayList(IntArrayList c) {
			size = c.size();
			data = c.data.clone();
		}

		public IntArrayList(int[] arr) {
			size = arr.length;
			data = arr.clone();
		}

		public int size() {
			return size;
		}

		public int get(int at) {
			if (at >= size) {
				throw new IndexOutOfBoundsException("at = " + at + ", size = " + size);
			}
			return data[at];
		}

		private void ensureCapacity(int capacity) {
			if (data.length >= capacity) {
				return;
			}
			capacity = Math.max(2 * data.length, capacity);
			data = Arrays.copyOf(data, capacity);
		}

		public void addAt(int index, int value) {
			ensureCapacity(size + 1);
			if (index > size || index < 0) {
				throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
			}
			if (index != size) {
				System.arraycopy(data, index, data, index + 1, size - index);
			}
			data[index] = value;
			size++;
		}

		public void removeAt(int index) {
			if (index >= size || index < 0) {
				throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
			}
			if (index != size - 1) {
				System.arraycopy(data, index + 1, data, index, size - index - 1);
			}
			size--;
		}

		public void set(int index, int value) {
			if (index >= size) {
				throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
			}
			data[index] = value;
		}

	}

	static class Sorter {
		private static final int INSERTION_THRESHOLD = 16;

		private Sorter() {
		}

		public static void sort(IntList list, IntComparator comparator) {
			quickSort(list, 0, list.size() - 1, (Integer.bitCount(Integer.highestOneBit(list.size()) - 1) * 5) >> 1, comparator);
		}

		private static void quickSort(IntList list, int from, int to, int remaining, IntComparator comparator) {
			if (to - from < INSERTION_THRESHOLD) {
				insertionSort(list, from, to, comparator);
				return;
			}
			if (remaining == 0) {
				heapSort(list, from, to, comparator);
				return;
			}
			remaining--;
			int pivotIndex = (from + to) >> 1;
			int pivot = list.get(pivotIndex);
			list.swap(pivotIndex, to);
			int storeIndex = from;
			int equalIndex = to;
			for (int i = from; i < equalIndex; i++) {
				int value = comparator.compare(list.get(i), pivot);
				if (value < 0) {
					list.swap(storeIndex++, i);
				} else if (value == 0) {
					list.swap(--equalIndex, i--);
				}
			}
			quickSort(list, from, storeIndex - 1, remaining, comparator);
			for (int i = equalIndex; i <= to; i++) {
				list.swap(storeIndex++, i);
			}
			quickSort(list, storeIndex, to, remaining, comparator);
		}

		private static void heapSort(IntList list, int from, int to, IntComparator comparator) {
			for (int i = (to + from - 1) >> 1; i >= from; i--) {
				siftDown(list, i, to, comparator, from);
			}
			for (int i = to; i > from; i--) {
				list.swap(from, i);
				siftDown(list, from, i - 1, comparator, from);
			}
		}

		private static void siftDown(IntList list, int start, int end, IntComparator comparator, int delta) {
			int value = list.get(start);
			while (true) {
				int child = ((start - delta) << 1) + 1 + delta;
				if (child > end) {
					return;
				}
				int childValue = list.get(child);
				if (child + 1 <= end) {
					int otherValue = list.get(child + 1);
					if (comparator.compare(otherValue, childValue) > 0) {
						child++;
						childValue = otherValue;
					}
				}
				if (comparator.compare(value, childValue) >= 0) {
					return;
				}
				list.swap(start, child);
				start = child;
			}
		}

		private static void insertionSort(IntList list, int from, int to, IntComparator comparator) {
			for (int i = from + 1; i <= to; i++) {
				int value = list.get(i);
				for (int j = i - 1; j >= from; j--) {
					if (comparator.compare(list.get(j), value) <= 0) {
						break;
					}
					list.swap(j, j + 1);
				}
			}
		}

	}

	static interface IntComparator {
		public static final IntComparator DEFAULT = (first, second) -> {
			if (first < second) {
				return -1;
			}
			if (first > second) {
				return 1;
			}
			return 0;
		};

		public int compare(int first, int second);

	}

	static class OutputWriter {
		private final PrintWriter writer;

		public OutputWriter(OutputStream outputStream) {
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}

		public OutputWriter(Writer writer) {
			this.writer = new PrintWriter(writer);
		}

		public void print(char i) {
			writer.print(i);
		}

		public void close() {
			writer.close();
		}

		public void printLine(int i) {
			writer.println(i);
		}

	}
}