Leonid works for a small and promising start-up that works on decoding the human genome. His duties include solving complex problems of finding certain patterns in long strings consisting of letters 'A', 'T', 'G' and 'C'.

Let's consider the following scenario. There is a fragment of a human DNA chain, recorded as a string S. To analyze the fragment, you need to find all occurrences of string T in a string S. However, the matter is complicated by the fact that the original chain fragment could contain minor mutations, which, however, complicate the task of finding a fragment. Leonid proposed the following approach to solve this problem.

Let's write down integer k ≥ 0 — the error threshold. We will say that string T occurs in string S on position i (1 ≤ i ≤ |S| - |T| + 1), if after putting string T along with this position, each character of string T corresponds to the some character of the same value in string S at the distance of at most k. More formally, for any j (1 ≤ j ≤ |T|) there must exist such p (1 ≤ p ≤ |S|), that |(i + j - 1) - p| ≤ k and S[p] = T[j].

For example, corresponding to the given definition, string "ACAT" occurs in string "AGCAATTCAT" in positions 2, 3 and 6.

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Note that at k = 0 the given definition transforms to a simple definition of the occurrence of a string in a string.

Help Leonid by calculating in how many positions the given string T occurs in the given string S with the given error threshold.

Input

The first line contains three integers |S|, |T|, k (1 ≤ |T| ≤ |S| ≤ 200 000, 0 ≤ k ≤ 200 000) — the lengths of strings S and T and the error threshold.

The second line contains string S.

The third line contains string T.

Both strings consist only of uppercase letters 'A', 'T', 'G' and 'C'.

Output

Print a single number — the number of occurrences of T in S with the error threshold k by the given definition.

Examples

Input

10 4 1
AGCAATTCAT
ACAT


Output

3

Note

If you happen to know about the structure of the human genome a little more than the author of the problem, and you are not impressed with Leonid's original approach, do not take everything described above seriously.
//package round296;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class D {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni(), m = ni(), K = ni();
		char[] s = ns(n);
		char[] t = ns(m);
		boolean[] ret = new boolean[n-m+1];
		Arrays.fill(ret, true);
		for(char c : "ATGC".toCharArray()){
			int[] imos = new int[n+1];
			for(int i = 0;i < n;i++){
				if(s[i] == c){
					imos[Math.max(i-K, 0)]++;
					imos[Math.min(n, i+K+1)]--;
				}
			}
			for(int i = 1;i <= n;i++){
				imos[i] += imos[i-1];
			}
			for(int i = 0;i <= n;i++){
				if(imos[i] > 1)imos[i] = 1;
			}
			
			int ap = 0;
			int[] tt = new int[m];
			for(int i = 0;i < m;i++){
				if(t[i] == c){
					tt[m-1-i] = 1;
					ap++;
				}
			}
			if(ap == 0)continue;
			
//			tr(c);
//			tr(imos);
//			tr(tt);
			long[] v = convolute(imos, tt);
//			tr(v);
			for(int i = 0;i < n-m+1;i++){
				if(v[i+m-1] != ap){
					ret[i] = false;
				}
			}
		}
		int re = 0;
		for(int i = 0;i < n-m+1;i++){
			if(ret[i])re++;
		}
		out.println(re);
	}
	
	public static long[] convolute(int[] a, int[] b)
	{
		int m = Integer.highestOneBit(Math.max(Math.max(a.length, b.length)-1, 1))<<2;
		double[][] fa = fft(a, m, false);
		double[][] fb = a == b ? fa : fft(b, m, false);
		for(int i = 0;i < m;i++){
			double nfa0 = fa[0][i]*fb[0][i]-fa[1][i]*fb[1][i];
			double nfa1 = fa[0][i]*fb[1][i]+fa[1][i]*fb[0][i];
			fa[0][i] = nfa0;
			fa[1][i] = nfa1;
		}
		fft(fa[0], fa[1], true);
		long[] ret = new long[m];
		for(int i = 0;i < m;i++){
			ret[i] = Math.round(fa[0][i]);
		}
		return ret;
	}
	
	public static double[][] fft(int[] srcRe, int n, boolean inverse)
	{
		int m = srcRe.length;
		double[] dstRe = new double[n];
		double[] dstIm = new double[n];
		for(int i = 0;i < m;i++){
			dstRe[i] = srcRe[i];
		}
		
		int h = Integer.numberOfTrailingZeros(n);
		for(int i = 0;i < n;i++){
			int rev = Integer.reverse(i)>>>32-h;
			if(i < rev){
				double d = dstRe[i]; dstRe[i] = dstRe[rev]; dstRe[rev] = d;
			}
		}
		
		for(int s = 2;s <= n;s <<= 1){
			int nt = s >>> 1;
			double theta = inverse ? -2*Math.PI/s : 2*Math.PI/s;
			double wRe = Math.cos(theta);
			double wIm = Math.sin(theta);
			for(int j = 0; j < n;j += s){
				double wr = 1, wi = 0;
				for(int t = j;t < j+nt;t++){
					int jp = t + nt;
					double re = dstRe[jp]*wr - dstIm[jp]*wi;
					double im = dstRe[jp]*wi + dstIm[jp]*wr;
					dstRe[jp] = dstRe[t] - re;
					dstIm[jp] = dstIm[t] - im;
					dstRe[t] += re;
					dstIm[t] += im;
					double nwre = wr * wRe - wi * wIm;
					double nwim = wr * wIm + wi * wRe;
					wr = nwre; wi = nwim;
				}
			}
		}
		
		if(inverse){
			for(int i = 0;i < n;i++){
				dstRe[i] /= n;
				dstIm[i] /= n;
			}
		}
		
		return new double[][]{dstRe, dstIm};
	}
	
	public static void fft(double[] re, double[] im, boolean inverse)
	{
		int n = re.length;
		int h = Integer.numberOfTrailingZeros(n);
		for(int i = 0;i < n;i++){
			int rev = Integer.reverse(i)>>>32-h;
			if(i < rev){
				double d = re[i]; re[i] = re[rev]; re[rev] = d;
				d = im[i]; im[i] = im[rev]; im[rev] = d;
			}
		}
		
		for(int s = 2;s <= n;s <<= 1){
			int nt = s >>> 1;
			double theta = inverse ? -2*Math.PI/s : 2*Math.PI/s;
			double wRe = Math.cos(theta);
			double wIm = Math.sin(theta);
			for(int j = 0; j < n;j += s){
				double wr = 1, wi = 0;
				for(int t = j;t < j+nt;t++){
					int jp = t + nt;
					double lre = re[jp]*wr - im[jp]*wi;
					double lim = re[jp]*wi + im[jp]*wr;
					re[jp] = re[t] - lre;
					im[jp] = im[t] - lim;
					re[t] += lre;
					im[t] += lim;
					double nwre = wr * wRe - wi * wIm;
					double nwim = wr * wIm + wi * wRe;
					wr = nwre; wi = nwim;
				}
			}
		}
		
		if(inverse){
			for(int i = 0;i < n;i++){
				re[i] /= n;
				im[i] /= n;
			}
		}
	}
	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new D().run(); }
	
	private byte[] inbuf = new byte[1024];
	private int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}
