Problem: One day Kefa the parrot was walking down the street as he was on the way home from the restaurant when he saw something glittering by the road. As he came nearer he understood that it was a watch. He decided to take it to the pawnbroker to earn some money. 

The pawnbroker said that each watch contains a serial number represented by a string of digits from 0 to 9, and the more quality checks this number passes, the higher is the value of the watch. The check is defined by three positive integers l, r and d. The watches pass a check if a substring of the serial number from l to r has period d. Sometimes the pawnbroker gets distracted and Kefa changes in some substring of the serial number all digits to c in order to increase profit from the watch. 

The seller has a lot of things to do to begin with and with Kefa messing about, he gave you a task: to write a program that determines the value of the watch.

Let us remind you that number x is called a period of string s (1 ≤ x ≤ |s|), if si = si + x for all i from 1 to |s| - x.

Input

The first line of the input contains three positive integers n, m and k (1 ≤ n ≤ 105, 1 ≤ m + k ≤ 105) — the length of the serial number, the number of change made by Kefa and the number of quality checks.

The second line contains a serial number consisting of n digits.

Then m + k lines follow, containing either checks or changes. 

The changes are given as 1 l r c (1 ≤ l ≤ r ≤ n, 0 ≤ c ≤ 9). That means that Kefa changed all the digits from the l-th to the r-th to be c. 

The checks are given as 2 l r d (1 ≤ l ≤ r ≤ n, 1 ≤ d ≤ r - l + 1).

Output

For each check on a single line print "YES" if the watch passed it, otherwise print "NO".

Examples

Input

3 1 2
112
2 2 3 1
1 1 3 8
2 1 2 1


Output

NO
YES


Input

6 2 3
334934
2 2 5 2
1 4 4 3
2 1 6 3
1 2 3 8
2 3 6 1


Output

NO
YES
NO

Note

In the first sample test two checks will be made. In the first one substring "12" is checked on whether or not it has period 1, so the answer is "NO". In the second one substring "88", is checked on whether or not it has period 1, and it has this period, so the answer is "YES".

In the second statement test three checks will be made. The first check processes substring "3493", which doesn't have period 2. Before the second check the string looks as "334334", so the answer to it is "YES". And finally, the third check processes substring "8334", which does not have period 1.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.awt.Point;
import java.math.BigDecimal;
import java.math.BigInteger;

import static java.lang.Math.*;


public class E implements Runnable{
	
	// SOLUTION!!! 
	// HACK ME PLEASE IF YOU CAN!!!
	// PLEASE!!!
	// PLEASE!!!
	// PLEASE!!!
	void solve() throws IOException {
		int n = readInt();
		int queriesCount = readInt() + readInt();
		
		int[] digits = new int[n];
		
		char[] digitCharacters = readCharArray();
		for (int i = 0; i < n; ++i) {
			digits[i] = digitCharacters[i] - '0' + 1;
		}
		
		SegmentTree tree = new SegmentTree(digits);
		
		final int CHANGE = 1, CHECK = 2;
		
		while (queriesCount --> 0) {
			int type = readInt();
			int left = readInt() - 1; 
			int right = readInt() - 1;
			int value = readInt();
			
			if (type == CHANGE) {
				tree.set(left, right, value + 1);
			} else if (type == CHECK) {
				boolean result = tree.isPeriod(left, right, value);
				out.println(result ? "YES" : "NO");
			}
		}
	}
	
	static class SegmentTree {
		static final int PRIME = 13, MODULO = 59815783;
		
		int size, treeSize;
		int[] powers, prefixPowerSums;
		int[] hashSegmentSums;
		
		int[] sizes;
		int[] lefts, rights, mids;
		int[] vLefts, vRights;
		
		int[] hashSums;
		int[] periods;
		
		int[] lazyColors;
		
		SegmentTree(int[] array) {
			this.size = array.length;
			this.treeSize = (size << 2);
			
			this.powers = new int[size + 2];
			powers[0] = 1;
			
			for (int power = 1; power < powers.length; ++power) {
				powers[power] = (int)((1L * powers[power - 1] * PRIME) % MODULO);
			}
			
			this.prefixPowerSums = new int[powers.length + 1];
			prefixPowerSums[0] = 0;
			
			for (int power = 1; power <= powers.length; ++power) {
				prefixPowerSums[power] = (prefixPowerSums[power - 1] + powers[power - 1]) % MODULO;
			}
			
			this.hashSegmentSums = new int[treeSize];
			
			this.sizes = new int[treeSize];
			
			this.hashSums = new int[treeSize];
			
			this.lazyColors = new int[treeSize];
			Arrays.fill(lazyColors, -1);
			
			this.lefts = new int[treeSize];
			this.rights = new int[treeSize];
			this.mids = new int[treeSize];
			
			this.vLefts = new int[treeSize];
			this.vRights = new int[treeSize];
			
			Arrays.fill(mids, treeSize);
			Arrays.fill(vLefts, treeSize);
			Arrays.fill(vRights, treeSize);
			
			init(1, 0, size - 1, array);
		}
		
		protected void init(int v, int left, int right, int[] array) {
			lefts[v] = left;
			rights[v] = right;
			
			hashSegmentSums[v] = (prefixPowerSums[rights[v] + 1] - prefixPowerSums[lefts[v]] + MODULO) % MODULO;
			
			if (left == right) {
				hashSums[v] = (int)((1L * array[left] * powers[left]) % MODULO);  
			} else {
				int mid = mids[v] = (left + right) >> 1;
			
				int vLeft = vLefts[v] = (v << 1);
				int vRight = vRights[v] = (vLeft + 1);
				
				init(vLeft, left, mid, array);
				init(vRight, mid + 1, right, array);
				
				hashSums[v] = (hashSums[vLeft] + hashSums[vRight]) % MODULO;
			}
		}
		
		protected void push(int v) {
			int color = lazyColors[v];
			if (color != -1) {
				
//				hashSums[v] = (color * hashSegmentSums[v]) % MODULO;
				
				int vLeft = vLefts[v];
				int vRight = vRights[v];
				
//				if (vRight < treeSize) {
					lazyColors[vLeft] = color;
					hashSums[vLeft] = (int)((1L * color * hashSegmentSums[vLeft]) % MODULO);
					
					lazyColors[vRight] = color;
					hashSums[vRight] = (int)((1L * color * hashSegmentSums[vRight]) % MODULO);
//				}
				
				lazyColors[v] = -1;
			}
		}
		
//		protected void update(int v) {
//			int vLeft = vLefts[v];
//			int vRight = vRights[v];
//			
//			push(vLeft);
//			push(vRight);
//			
//			hashSums[v] = (hashSums[vLeft] + hashSums[vRight]) % MODULO;
//		}
		
		public boolean isPeriod(int left, int right, int delta) {
			int size = (right - left + 1);
			
			boolean leftResult = areEqualSubstrings(left, right - size % delta - delta, left + delta, right - size % delta);
			boolean rightResult = areEqualSubstrings(left + size % delta, right - delta, left + size % delta + delta, right);
			
			boolean isPeriod = (leftResult & rightResult);
			if (size % delta != 0) {
				isPeriod &= areEqualSubstrings(left, left + size % delta - 1, right - size % delta + 1, right);
			}
			
			return isPeriod;
		}
		
		protected boolean areEqualSubstrings(int l1, int r1, int l2, int r2) {
			long hash1 = getHash(l1, r1);
			long hash2 = getHash(l2, r2);
			
			hash1 = (hash1  % MODULO * powers[l2 - l1]) % MODULO;
			hash2 %= MODULO;
			
			return (hash1 == hash2);
		}
		
		protected int getHash(int left, int right) {
			return get(1, left, right);
		}
		
		protected int get(int v, int qLeft, int qRight) {
			int left = lefts[v];
			int right = rights[v];
			
			if (qRight < left || right < qLeft) {
				return 0;
			}
			
//			push(v);
			
			if (left == qLeft && right == qRight) {
				return hashSums[v];
			} else {
				push(v);
				
				int mid = mids[v];
				
				int vLeft = vLefts[v];
				int vRight = vRights[v];
				
				int hashSum = -1;
				if (qRight <= mid) {
					hashSum = get(vLeft, qLeft, qRight);
				} else if (qLeft > mid) {
					hashSum = get(vRight, qLeft, qRight);
				} else {
					int leftHashSum = (qLeft <= mid ? get(vLeft, qLeft, mid) : 0);
					int rightHashSum = (qRight > mid ? get(vRight, mid + 1, qRight) : 0);
					
					hashSum = (leftHashSum + rightHashSum);// % MODULO;
				}
//				int leftHashSum = (qLeft <= mid ? get(vLeft, qLeft, min(mid, qRight)) : 0);
//				int rightHashSum = (qRight > mid ? get(vRight, max(qLeft, mid + 1), qRight) : 0);
//				
//				int hashSum = (leftHashSum + rightHashSum);// % MODULO;
				
				hashSums[v] = (hashSums[vLeft] + hashSums[vRight]) % MODULO;
//				update(v);
				
				return hashSum;
			}
		}
		
		public void set(int left, int right, int color) {
			set(1, left, right, color);
		}
		
		protected void set(int v, int qLeft, int qRight, int color) {
			int left = lefts[v];
			int right = rights[v];
			
			if (qRight < left || right < qLeft) {
				return;
			}
			
			if (left == qLeft && right == qRight) {
				lazyColors[v] = color;
				hashSums[v] = (int)((1L * color * hashSegmentSums[v]) % MODULO);
//				push(v);
			} else {
				push(v);
				
				int mid = mids[v];
				
				int vLeft = vLefts[v];
				int vRight = vRights[v];
				
				if (qLeft <= mid) set(vLeft, qLeft, min(mid, qRight), color);
				if (qRight > mid) set(vRight, max(qLeft, mid + 1), qRight, color);
				
				//update(v);
				hashSums[v] = (hashSums[vLeft] + hashSums[vRight]) % MODULO;
			}
		}
	}
	
	/////////////////////////////////////////////////////////////////////
	
	final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
	
	BufferedReader in;
	OutputWriter out;
	StringTokenizer tok = new StringTokenizer("");
	
	public static void main(String[] args){
		new Thread(null, new E(), "", 128 * (1L << 20)).start();
	}
	
	/////////////////////////////////////////////////////////////////////
	
	void init() throws FileNotFoundException{
		Locale.setDefault(Locale.US);
		
		if (ONLINE_JUDGE){
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new OutputWriter(System.out);
		}else{
			in = new BufferedReader(new FileReader("input.txt"));
			out = new OutputWriter("output.txt");
		}
	}
	
	////////////////////////////////////////////////////////////////
	
	long timeBegin, timeEnd;

	void time(){
		timeEnd = System.currentTimeMillis();
		System.err.println("Time = " + (timeEnd - timeBegin));
	}
	
	void debug(Object... objects){
		if (ONLINE_JUDGE){
			for (Object o: objects){
				System.err.println(o.toString());
			}
		}
	}
	
	/////////////////////////////////////////////////////////////////////
	
	public void run(){
		try{
			timeBegin = System.currentTimeMillis();
			Locale.setDefault(Locale.US);
			
			init();
			
			if (ONLINE_JUDGE) {
				solve();
			} else {
				while (true) {
					try {
						solve();
					} catch (NumberFormatException e) {
						break;
					}
				}
			}
			
			out.close();
			time();
		}catch (Exception e){
			e.printStackTrace(System.err);
			System.exit(-1);
		}
	}
	
	/////////////////////////////////////////////////////////////////////
	
	String delim = " ";
	
	String readString() throws IOException{
		while(!tok.hasMoreTokens()){
			try{
				tok = new StringTokenizer(in.readLine());
			}catch (Exception e){
				return null;
			}
		}
		
		return tok.nextToken(delim);
	}
	
	String readLine() throws IOException{
		return in.readLine();
	}
	
	/////////////////////////////////////////////////////////////////
	
	final char NOT_A_SYMBOL = '\0';
	
	char readChar() throws IOException{
		int intValue = in.read();
		
		if (intValue == -1){
			return NOT_A_SYMBOL;
		}
		
		return (char) intValue;
	}
	
	char[] readCharArray() throws IOException{
		return readLine().toCharArray();
	}
	
	/////////////////////////////////////////////////////////////////
	
	int readInt() throws IOException {
		return Integer.parseInt(readString());
	}
	
	int[] readIntArray(int size) throws IOException {
		int[] array = new int[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readInt();
		}
		
		return array;
	}
	
	int[] readSortedIntArray(int size) throws IOException {
		Integer[] array = new Integer[size];
		
		for (int index = 0; index < size; ++index) {
			array[index] = readInt();
		}
		Arrays.sort(array);
		
		int[] sortedArray = new int[size];
		for (int index = 0; index < size; ++index) {
			sortedArray[index] = array[index];
		}
		
		return sortedArray;
	}
	
	int[] readIntArrayWithDecrease(int size) throws IOException {
		int[] array = readIntArray(size);
		
		for (int i = 0; i < size; ++i) {
			array[i]--;
		}
		
		return array;
	}
	
	///////////////////////////////////////////////////////////////////
	
	int[][] readIntMatrix(int rowsCount, int columnsCount) throws IOException {
		int[][] matrix = new int[rowsCount][];
		
		for (int rowIndex = 0; rowIndex < rowsCount; ++rowIndex) {
			matrix[rowIndex] = readIntArray(columnsCount);
		}
		
		return matrix;
	}
	
	int[][] readIntMatrixWithDecrease(int rowsCount, int columnsCount) throws IOException {
		int[][] matrix = new int[rowsCount][];
		
		for (int rowIndex = 0; rowIndex < rowsCount; ++rowIndex) {
			matrix[rowIndex] = readIntArrayWithDecrease(columnsCount);
		}
		
		return matrix;
	}
	
	///////////////////////////////////////////////////////////////////
	
	long readLong() throws IOException{
		return Long.parseLong(readString());
	}
	
	long[] readLongArray(int size) throws IOException{
		long[] array = new long[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readLong();
		}
		
		return array;
	}
	
	////////////////////////////////////////////////////////////////////
	
	double readDouble() throws IOException{
		return Double.parseDouble(readString());
	}
	
	double[] readDoubleArray(int size) throws IOException{
		double[] array = new double[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readDouble();
		}
		
		return array;
	}
	
	////////////////////////////////////////////////////////////////////
		
	BigInteger readBigInteger() throws IOException {
		return new BigInteger(readString());
	}
	
	BigDecimal readBigDecimal() throws IOException {
		return new BigDecimal(readString());
	}
	
	/////////////////////////////////////////////////////////////////////
	
	Point readPoint() throws IOException{
		int x = readInt();
		int y = readInt();
		return new Point(x, y);
	}
	
	Point[] readPointArray(int size) throws IOException{
		Point[] array = new Point[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readPoint();
		}
		
		return array;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	List<Integer>[] readGraph(int vertexNumber, int edgeNumber)
	throws IOException{
		@SuppressWarnings("unchecked")
		List<Integer>[] graph = new List[vertexNumber];
		
		for (int index = 0; index < vertexNumber; ++index){
			graph[index] = new ArrayList<Integer>();
		}
		
		while (edgeNumber-- > 0){
			int from = readInt() - 1;
			int to = readInt() - 1;
			
			graph[from].add(to);
			graph[to].add(from);
		}
		
		return graph;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	static class IntIndexPair {
		
		static Comparator<IntIndexPair> increaseComparator = new Comparator<IntIndexPair>() {
			
			@Override
			public int compare(IntIndexPair indexPair1, IntIndexPair indexPair2) {
				int value1 = indexPair1.value;
				int value2 = indexPair2.value;
				
				if (value1 != value2) return value1 - value2;
				
				int index1 = indexPair1.index;
				int index2 = indexPair2.index;
				
				return index1 - index2;
			}
		};
		
		static Comparator<IntIndexPair> decreaseComparator = new Comparator<IntIndexPair>() {
			
			@Override
			public int compare(IntIndexPair indexPair1, IntIndexPair indexPair2) {
				int value1 = indexPair1.value;
				int value2 = indexPair2.value;
				
				if (value1 != value2) return -(value1 - value2);
				
				int index1 = indexPair1.index;
				int index2 = indexPair2.index;
				
				return index1 - index2;
			}
		};
		
		int value, index;

		public IntIndexPair(int value, int index) {
			super();
			this.value = value;
			this.index = index;
		}		
		
		public int getRealIndex() {
			return index + 1;
		}
	}
	
	IntIndexPair[] readIntIndexArray(int size) throws IOException {
		IntIndexPair[] array = new IntIndexPair[size];
		
		for (int index = 0; index < size; ++index) {
			array[index] = new IntIndexPair(readInt(), index);
		}
		
		return array;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	static class OutputWriter extends PrintWriter {

		final int DEFAULT_PRECISION = 12;
		
		protected int precision;
		protected String format, formatWithSpace;
		
		{
			precision = DEFAULT_PRECISION;
			
			format = createFormat(precision);
			formatWithSpace = format + " ";
		}
		
		public OutputWriter(OutputStream out) {
			super(out);
		}

		public OutputWriter(String fileName) throws FileNotFoundException {
			super(fileName);
		}
		
		public int getPrecision() {
			return precision;
		}

		public void setPrecision(int precision) {
			precision = max(0, precision);
			this.precision = precision;
			
			format = createFormat(precision);
			formatWithSpace = format + " ";
		}
		
		private String createFormat(int precision){
			return "%." + precision + "f";
		}
		
		@Override
		public void print(double d){
			printf(format, d);
		}
		
		public void printWithSpace(double d){
			printf(formatWithSpace, d);
		}

		public void printAll(double...d){
			for (int i = 0; i < d.length - 1; ++i){
				printWithSpace(d[i]);
			}
			
			print(d[d.length - 1]);
		}
		
		@Override
		public void println(double d){
			printlnAll(d);
		}
		
		public void printlnAll(double... d){
			printAll(d);
			println();
		}
	}
	
	/////////////////////////////////////////////////////////////////////
	
	static final int[][] steps = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}}; 
	static final int[][] steps8 = {
			{-1, 0}, {1, 0}, {0, -1}, {0, 1},
			{-1, -1}, {1, 1}, {1, -1}, {-1, 1}
	};
	
	static final boolean check(int index, int lim){
		return (0 <= index && index < lim);
	}
	
	/////////////////////////////////////////////////////////////////////
	
	static final boolean checkBit(int mask, int bit){
		return (mask & (1 << bit)) != 0;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	static final long getSum(int[] array) {
		long sum = 0;
		for (int value: array) {
			sum += value;
		}
		
		return sum;
	}
	
	static final Point getMinMax(int[] array) {
		int min = array[0];
		int max = array[0];
		
		for (int index = 0, size = array.length; index < size; ++index, ++index) {
			int value = array[index];
			
			if (index == size - 1) {
				min = min(min, value);
				max = max(max, value);
			} else {
				int otherValue = array[index + 1];
				
				if (value <= otherValue) {
					min = min(min, value);
					max = max(max, otherValue);
				} else {
					min = min(min, otherValue);
					max = max(max, value);
				}
			}
		}
		
		return new Point(min, max);
	}
}