Problem: Limak is a little polar bear. His parents told him to clean a house before the New Year's Eve. Their house is a rectangular grid with h rows and w columns. Each cell is an empty square.

He is a little bear and thus he can't clean a house by himself. Instead, he is going to use a cleaning robot.

A cleaning robot has a built-in pattern of n moves, defined by a string of the length n. A single move (character) moves a robot to one of four adjacent cells. Each character is one of the following four: 'U' (up), 'D' (down), 'L' (left), 'R' (right). One move takes one minute.

A cleaning robot must be placed and started in some cell. Then it repeats its pattern of moves till it hits a wall (one of four borders of a house). After hitting a wall it can be placed and used again.

Limak isn't sure if placing a cleaning robot in one cell will be enough. Thus, he is going to start it w·h times, one time in each cell. Maybe some cells will be cleaned more than once but who cares?

Limak asks you one question. How much time will it take to clean a house? Find and print the number of minutes modulo 109 + 7. It's also possible that a cleaning robot will never stop — then print "-1" (without the quotes) instead.

Placing and starting a robot takes no time, however, you must count a move when robot hits a wall. Take a look into samples for further clarification.

Input

The first line contains three integers n, h and w (1 ≤ n, h, w ≤ 500 000) — the length of the pattern, the number of rows and the number of columns, respectively.

The second line contains a string of length n — the pattern of n moves. Each character is one of uppercase letters 'U', 'D', 'L' or 'R'.

Output

Print one line with the answer.

If a cleaning robot will never stop, print "-1" (without the quotes). Otherwise, print the number of minutes it will take to clean a house modulo 109 + 7.

Examples

Input

1 10 2
R


Output

30


Input

3 4 6
RUL


Output

134


Input

4 1 500000
RLRL


Output

-1

Note

In the first sample house is a grid with 10 rows and 2 columns. Starting a robot anywhere in the second column will result in only one move (thus, one minute of cleaning) in which robot will hit a wall — he tried to go right but there is no third column. Starting a robot anywhere in the first column will result in two moves. The total number of minutes is 10·1 + 10·2 = 30.

In the second sample a started robot will try to move "RULRULRULR..." For example, for the leftmost cell in the second row robot will make 5 moves before it stops because of hitting an upper wall.

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 {
		private static final long MOD = (long) (1e9 + 7);

		public void solve(int testNumber, InputReader in, OutputWriter out) {
			int n = in.readInt();
			int h = in.readInt();
			int w = in.readInt();
			char[] template = IOUtils.readCharArray(in, n);
			int l = 0;
			int r = 0;
			int u = 0;
			int d = 0;
			int x = 0;
			int y = 0;
			IntList rs = new IntArrayList();
			IntList ls = new IntArrayList();
			IntList us = new IntArrayList();
			IntList ds = new IntArrayList();
			long answer = 0;
			for (int i = 0; i < n; i++) {
				if (template[i] == 'U') {
					y++;
				} else if (template[i] == 'D') {
					y--;
				} else if (template[i] == 'L') {
					x--;
				} else if (template[i] == 'R') {
					x++;
				}
				if (x < l) {
					l = x;
					ls.add(i + 1);
					answer += (long) (i + 1) * h;
					w--;
				} else if (x > r) {
					r = x;
					rs.add(i + 1);
					answer += (long) (i + 1) * h;
					w--;
				} else if (y < d) {
					d = y;
					ds.add(i + 1);
					answer += (long) (i + 1) * w;
					h--;
				} else if (y > u) {
					u = y;
					us.add(i + 1);
					answer += (long) (i + 1) * w;
					h--;
				}
				answer %= MOD;
				if (w == 0 || h == 0) {
					out.printLine(answer);
					return;
				}
			}
			if (x == 0 && y == 0) {
				out.printLine(-1);
				return;
			}
			IntList at = new IntArrayList();
			IntList dir = new IntArrayList();
			if (x > 0) {
				at.addAll(rs.subList(rs.size() - x, rs.size()));
				dir.addAll(new IntArray(new int[x]));
			} else if (x < 0) {
				at.addAll(ls.subList(ls.size() + x, ls.size()));
				dir.addAll(new IntArray(new int[-x]));
			}
			if (y > 0) {
				at.addAll(us.subList(us.size() - y, us.size()));
				dir.addAll(new IntArray(ArrayUtils.createArray(y, 1)));
			} else if (y < 0) {
				at.addAll(ds.subList(ds.size() + y, ds.size()));
				dir.addAll(new IntArray(ArrayUtils.createArray(-y, 1)));
			}
			int[] aa = at.toArray();
			int[] dd = dir.toArray();
			ArrayUtils.orderBy(aa, dd);
			for (long add = n; ; add += n) {
				for (int i = 0; i < aa.length; i++) {
					if (dd[i] == 0) {
						answer += (add + aa[i]) % MOD * h;
						w--;
					} else {
						answer += (add + aa[i]) % MOD * w;
						h--;
					}
					answer %= MOD;
					if (w == 0 || h == 0) {
						out.printLine(answer);
						return;
					}
				}
			}
		}

	}

	static interface IntComparator {
		public int compare(int first, int second);

	}

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

		public boolean advance();

		public boolean isValid();

	}

	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 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 IntReversableCollection extends IntCollection {
	}

	static class Range {
		public static IntList range(int from, int to) {
			int[] result = new int[Math.abs(from - to)];
			int current = from;
			if (from <= to) {
				for (int i = 0; i < result.length; i++) {
					result[i] = current++;
				}
			} else {
				for (int i = 0; i < result.length; i++) {
					result[i] = current--;
				}
			}
			return new IntArray(result);
		}

	}

	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 close() {
			writer.close();
		}

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

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

	}

	static class ArrayUtils {
		private static int[] tempInt = new int[0];

		public static int[] range(int from, int to) {
			return Range.range(from, to).toArray();
		}

		public static int[] createOrder(int size) {
			return range(0, size);
		}

		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;
		}

		private static void ensureCapacityInt(int size) {
			if (tempInt.length >= size)
				return;
			size = Math.max(size, tempInt.length << 1);
			tempInt = new int[size];
		}

		public static int[] order(final int[] array) {
			return sort(createOrder(array.length), new IntComparator() {
				public int compare(int first, int second) {
					if (array[first] < array[second])
						return -1;
					if (array[first] > array[second])
						return 1;
					return 0;
				}
			});
		}

		public static void orderBy(int[] base, int[]... arrays) {
			int[] order = ArrayUtils.order(base);
			order(order, base);
			for (int[] array : arrays)
				order(order, array);
		}

		public static void order(int[] order, int[] array) {
			ensureCapacityInt(order.length);
			for (int i = 0; i < order.length; i++)
				tempInt[i] = array[order[i]];
			System.arraycopy(tempInt, 0, array, 0, array.length);
		}

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

	}

	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 char readCharacter() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			return (char) c;
		}

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

		}

	}

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

	}

	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 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 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 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;
		}

	}

	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 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;
		}

	}
}