Problem: Ilya got tired of sports programming, left university and got a job in the subway. He was given the task to determine the escalator load factor. 

Let's assume that n people stand in the queue for the escalator. At each second one of the two following possibilities takes place: either the first person in the queue enters the escalator with probability p, or the first person in the queue doesn't move with probability (1 - p), paralyzed by his fear of escalators and making the whole queue wait behind him.

Formally speaking, the i-th person in the queue cannot enter the escalator until people with indices from 1 to i - 1 inclusive enter it. In one second only one person can enter the escalator. The escalator is infinite, so if a person enters it, he never leaves it, that is he will be standing on the escalator at any following second. Ilya needs to count the expected value of the number of people standing on the escalator after t seconds. 

Your task is to help him solve this complicated task.

Input

The first line of the input contains three numbers n, p, t (1 ≤ n, t ≤ 2000, 0 ≤ p ≤ 1). Numbers n and t are integers, number p is real, given with exactly two digits after the decimal point.

Output

Print a single real number — the expected number of people who will be standing on the escalator after t seconds. The absolute or relative error mustn't exceed 10 - 6.

Examples

Input

1 0.50 1


Output

0.5


Input

1 0.50 4


Output

0.9375


Input

4 0.20 2


Output

0.4

Solution (in JAVA):

Solution:
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.io.ObjectInputStream.GetField;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Stack;
import java.util.TreeMap;
import java.util.TreeSet;
public class Q1 {
	
	static long MOD = 1000000007;
	static boolean b[],bc[];
	static boolean boo[][][];
	static ArrayList<Integer>[] amp,amp1;
	static int sum[],dist[],cnt[];
	static long ans = 0;
	static int p = 0;
	//static ArrayList<Pair3>[][][] pmp;
	static FasterScanner sc = new FasterScanner();
	static Queue<Integer> q = new LinkedList<>();
	static int arr[],start[],color[];
	static PriorityQueue<Integer> pq;
	//static ArrayList<Integer> parent = new ArrayList<>();
	static LinkedList<Integer> fa;
	static BufferedWriter log;
	static TreeMap<Integer,Integer> tm = new TreeMap<>();
	static HashSet<Integer> hs = new HashSet<>();
	static Stack<Integer> stack = new Stack<>();
	static Pair prr[];
	static long parent1[],parent2[],size[][],size1[],size2[];
	public static void main(String[] args) throws Exception {
    	new Thread(null, new Runnable() {
			public void run() {
				try {
					soln();
				} catch (Exception e) {
					e.printStackTrace();
				}
			}
		}, "1", 1 << 26).start();
    }
	private static Comparator<String> ALPHABETICAL_ORDER = new Comparator<String>() {
	    public int compare(String str1, String str2) {
	        int res = String.CASE_INSENSITIVE_ORDER.compare(str1, str2);
	        if (res == 0) {
	            res = str1.compareTo(str2);
	        }
	        if(str1.length()>str2.length() && str1.substring(0, str2.length()).equals(str1)){
	        	return 1;
	        }
	        return res;
	    }
	};
	public static class ExampleComparator  implements Comparator<String> {
		  public int compare(String obj1, String obj2) {
			StringBuilder sb = new StringBuilder();
			sb.append(obj1);sb.append(obj2);
			StringBuilder sb2 = new StringBuilder();
			sb2.append(obj2);sb2.append(obj1);
		    if (sb.toString() == sb2.toString()) {
		        return 0;
		    }
		    return sb.toString().compareTo(sb2.toString());
		  }
		}
	public static void soln() throws IOException {
		log = new BufferedWriter(new OutputStreamWriter(System.out));
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		double p = sc.nextDouble(), p1 = 1-p;
		int t = sc.nextInt();
		double fa = 0;
		double dp[][] = new double[n+1][t+1];
		for(int i =1 ;i <=n ;i++){
			for(int j = i ;j<=t;j++){
				if(i==1 && j==1){
					dp[i][j] = p;
					fa+=dp[i][j];
					continue;
				}
				dp[i][j] = (dp[i][j-1]*p1+dp[i-1][j-1]*p);
				fa+=dp[i][j];
			}
		}
		System.out.println(fa);
		log.close();
	}
	public static int binarySearch(long arr[],long key){
		int low = 0, high = arr.length-1;
		while(low<high){
			int mid = (high+low+1)/2;
			if(arr[mid] >= key) low = mid;
			else high = mid-1;
		}
		if(arr[low]<key)
		return low+1;
		else return 0;
	}
	public static void bfs(int x,int arr[]){
	b = new boolean[arr.length];
	b[x] = true;
	q = new LinkedList<>();
	q.add(x);
	while(!q.isEmpty()){
		int y = q.poll();
		for(int i = 0;i<amp[y].size();i++) {
			if(!b[amp[y].get(i)]){
				q.add(amp[y].get(i));
				b[amp[y].get(i)] = true;
				arr[amp[y].get(i)] = (arr[y]+1);
			}
		}
	}
	}
	
	static long get(long x){
		if((x%10)<5) return x-(x%10);
		else return x+(10-x%10);
	}
	static int startTime = 0;
	public static void dfs(int x){
		start[x] = startTime++;
		b[x] = true;
		for(int e:amp[x]){
			if(!b[e]){
				if(x==0){
					color[e] = ++p;
				}
				else color[e] = color[x];
				dfs(e);
				if(x==0) tm.put(color[e], (cnt[e]+1));
				cnt[x] = Math.max(cnt[x],cnt[e]);
			}
		}
		cnt[x]++;
	}
	static long func(long n, long d, long t){
		return (t*(2*(n-1)+(t-1)*(d)))/2;
	}
	static class Pair implements Comparable<Pair> {
		long u;
		long v;
		public Pair(long u, long v) {
			this.u = u;
			this.v = v;
		}
		
		public int hashCode() {
			int hu = (int) (u ^ (u >>> 32));
			int hv = (int) (v ^ (v >>> 32));
			return 31*hu + hv;
		}
 
		public boolean equals(Object o) {
			Pair other = (Pair) o;
			return (u == other.u && v == other.v);
		}
 
		public int compareTo(Pair other) {
			return Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)) : (Long.compare(v, other.v));
		}
		
		public String toString() {
			return "[u=" + u + ", v=" + v + "]";
		}
	}
	public static void buildGraph(int n){
		for(int i =0;i<n;i++){
			int x = sc.nextInt(), y = sc.nextInt();
			amp[--x].add(--y);
			amp[y].add(x);
		}
	}
	
	
	public static long getParent(long x, long parent[]){
		while(parent[(int) x]!=x){
			parent[(int) x] = parent[(int) parent[(int) x]];
			x = parent[(int) x];
		}
		return x;
	}
	static long min(long a, long b, long c){
		if(a<b && a<c) return a;
		if(b<c) return b;
		return c;
	}
	/*
	static void dfs3D(int x,int y,int z){
		ans++;
		boo[x][y][z] = true;
		for(Pair3 e:pmp[x][y][z]){
			if(!boo[e.x][e.y][e.z]){
				dfs3D(e.x,e.y,e.z);
			}
		}
	}
	static class Pair3{
		int x, y ,z;
		Pair3(int x, int y, int z){
			this.x = x;
			this.y = y;
			this.z = z;
		}
	}*/
	static int sum(int n){
		String str = Integer.toString(n);
		int cnt = 0;
		for(int i = 0; i< str.length();i++){
			cnt+=(str.charAt(i)-'0');
		}
		return cnt;
	}
	 static void KMPSearch(String pat, String txt)
	    {
	        int M = pat.length();
	        int N = txt.length();
	 
	        // create lps[] that will hold the longest
	        // prefix suffix values for pattern
	        int lps[] = new int[M];
	        int j = 0;  // index for pat[]
	 
	        // Preprocess the pattern (calculate lps[]
	        // array)
	        computeLPSArray(pat,M,lps);
	 
	        int i = 0;  // index for txt[]
	        while (i < N)
	        {
	            if (pat.charAt(j) == txt.charAt(i))
	            {
	                j++;
	                i++;
	            }
	            if (j == M)
	            {
	               // parent.add((i-j));
	                j = lps[j-1];
	            }
	 
	            // mismatch after j matches
	            else if (i < N && pat.charAt(j) != txt.charAt(i))
	            {
	                // Do not match lps[0..lps[j-1]] characters,
	                // they will match anyway
	                if (j != 0)
	                    j = lps[j-1];
	                else
	                    i = i+1;
	            }
	        }
	    }
	 static void computeLPSArray(String pat, int M, int lps[])
	    {
	        // length of the previous longest prefix suffix
	        int len = 0;
	        int i = 1;
	        lps[0] = 0;  // lps[0] is always 0
	 
	        // the loop calculates lps[i] for i = 1 to M-1
	        while (i < M)
	        {
	            if (pat.charAt(i) == pat.charAt(len))
	            {
	                len++;
	                lps[i] = len;
	                i++;
	            }
	            else  // (pat[i] != pat[len])
	            {
	                // This is tricky. Consider the example.
	                // AAACAAAA and i = 7. The idea is similar 
	                // to search step.
	                if (len != 0)
	                {
	                    len = lps[len-1];
	 
	                    // Also, note that we do not increment
	                    // i here
	                }
	                else  // if (len == 0)
	                {
	                    lps[i] = len;
	                    i++;
	                }
	            }
	        }
	    }
	private static void permutation(String prefix, String str) {
	    int n = str.length();
	    if (n == 0); //hs.add(prefix);
	    else {
	        for (int i = 0; i < n; i++)
	            permutation(prefix + str.charAt(i), str.substring(0, i) + str.substring(i+1, n));
	    }
	}
	public static char give(char c1,char c2){
		if(c1!='a' && c2!='a') return 'a';
		if(c1!='b' && c2!='b') return 'b';
		return 'c';
	}
	static class Graph{
		int vertex;
		long weight;
	}
	public static void buildTree(int n){
		int arr[] = sc.nextIntArray(n);
		for(int i = 0;i<n;i++){
			int x = arr[i]-1;
			amp[i+1].add(x);
			amp[x].add(i+1);
		}
	}
	
	
	static class SegmentTree{
		int pre[], suf[], max[], val[];
		SegmentTree( int n){
			int size = 4*n;
			pre = new int[size];
			suf = new int[size];
			max = new int[size];
			val = new int[size];
			build(0,n-1,1);
		}
		void build(int ss, int se, int si){
			if(ss==se){
				pre[si] = 1;
				suf[si] = 1;
				max[si] = 1;
				val[si] = arr[ss];
			}
			else{
			int mid = (ss+se)>>2;
			si*=2;
			build(ss,mid,si);build(mid+1,se,si+1);
			}
		}
		
		/*int[] get(int qs, int qe, int ss, int se, int si){
			if(qe < ss || se < qs)
        		return new int[2];
			if(qs<=ss && qe>=se){
				return new int[]{max[si],val[si]};
			}
			int mid = (ss+se)/2;
			si*=2;
			if(qe<=mid) return get(qs,qe,ss,mid,si);
			else if(qs>mid) return get(qs,qe,mid+1,se,si+1);
			long a1[] = build(ss,mid,si*2), a2[] = build(mid+1,se,si*2+1);
			long ans[] = new long[4];
			if(arr[mid] == arr[mid+1]){
			    long temp = a1[2]+a2[0];
			    if(temp>=a2[1] && temp>=a1[1]){
			        ans[1] = temp;
			        ans[3] = arr[mid];
			    }
			    else if(a2[1]>=a1[1]){
			        ans[1] = a2[1];
			        ans[3] = a2[3];
			    }
			    else{
			        ans[1] = a1[1];
			        ans[3] = a1[3];
			    } 
			    if(a1[1]==(mid-ss+1)) ans[0] = ans[1];
			    else ans[0] = a1[0];
			    if(a2[2]==(se-mid)) ans[2] = ans[1];
				else ans[2] = a2[2];
			}
			else{
				if(a2[1]>=a1[1]){
			        ans[1] = a2[1];
			        ans[3] = a2[3];
			    }
			    else{
			        ans[1] = a1[1];
			        ans[3] = a1[3];
			    } 
				ans[0] = a1[0];
				ans[2] = a2[2];
			}
            return ans;
		}
		void print(){
			for(int i = 0;i<st.length;i++){
				System.out.println(st[i][0]+" "+st[i][1]+" "+st[i][2]+" "+st[i][3]);
			}
			System.out.println();
		}*/
	}
	static int convert(int x){
		int cnt = 0;
		String str = Integer.toBinaryString(x);
		//System.out.println(str);
		for(int i = 0;i<str.length();i++){
			if(str.charAt(i)=='1'){
				cnt++;
			}
		}
		int ans = (int) Math.pow(3, 6-cnt);
		return ans;
	}
	static class Node2{
		Node2 left = null;
		Node2 right = null;
		Node2 parent = null;
		int data;
	}
	static class BinarySearchTree{
		Node2 root = null;
		int height = 0;
		int max = 0;
		int cnt = 1;
		ArrayList<Integer> parent = new ArrayList<>();
		HashMap<Integer, Integer> hm = new HashMap<>();
		public void insert(int x){
			Node2 n = new Node2();
			n.data = x;
			if(root==null){
				root = n;
			}
			else{
				Node2 temp = root,temp2 = null;
				while(temp!=null){
					temp2 = temp;
					if(x>temp.data) temp = temp.right;
					else temp = temp.left;
				}
				if(x>temp2.data) temp2.right = n;
				else temp2.left = n;
				n.parent = temp2;
				parent.add(temp2.data);
			}
		}
		public Node2 getSomething(int x, int y, Node2 n){
			if(n.data==x || n.data==y) return n;
			else if(n.data>x && n.data<y) return n;
			else if(n.data<x && n.data<y) return getSomething(x,y,n.right);
			else return getSomething(x,y,n.left);
		}
		public Node2 search(int x,Node2 n){
			if(x==n.data){
				max = Math.max(max, n.data);
				return n;
			}
			if(x>n.data){
				max = Math.max(max, n.data);
				return search(x,n.right);
			}
			else{
				max = Math.max(max, n.data);
				return search(x,n.left);
			}
		}
		public int getHeight(Node2 n){
			if(n==null) return 0;
			height = 1+ Math.max(getHeight(n.left), getHeight(n.right));
			return height;
		}
	}
	static long findDiff(long[] arr, long[] brr, int m){
		int i = 0, j = 0;
		long fa = 1000000000000L;
		while(i<m && j<m){
			long x = arr[i]-brr[j];
			if(x>=0){
				if(x<fa) fa = x;
				j++;
			}
			else{
				if((-x)<fa) fa = -x;
				i++;
			}
		}
		return fa;
	}
	public static long max(long x, long y, long z){
		if(x>=y && x>=z) return x;
		if(y>=x && y>=z) return y;
		return z;
	}
	
	public static void seive(long n){
		b = new boolean[(int) (n+1)];
		Arrays.fill(b, true);
		for(int i = 2;i*i<=n;i++){
			if(b[i]){
				for(int p = 2*i;p<=n;p+=i){
					b[p] = false;
				}
			}
		}
	}
	static long modInverse(long a, long mOD2){
	            return  power(a, mOD2-2, mOD2);
	}
	static long power(long x, long y, long m)
	{
	    if (y == 0)
	        return 1;
	    long p = power(x, y/2, m) % m;
	    p = (p * p) % m;
	 
	    return (y%2 == 0)? p : (x * p) % m;
	}
	static long power2(long x,BigInteger y,long m){
		long ans = 1;
		BigInteger two = new BigInteger("2");
		while(y.compareTo(BigInteger.ZERO)>0){
			if(y.getLowestSetBit()==y.bitCount()){
				x = (x*x)%MOD;
				y = y.divide(two);
			}
			else{
				ans = (ans*x)%MOD;
				y = y.subtract(BigInteger.ONE);
			}
		}
		return ans;
	}
	static BigInteger power2(BigInteger x, BigInteger y, BigInteger m){
		BigInteger ans = new BigInteger("1");
		BigInteger one  = new BigInteger("1");
		BigInteger two  = new BigInteger("2");
		BigInteger zero  = new BigInteger("0");
		while(y.compareTo(zero)>0){
			//System.out.println(y);
			if(y.mod(two).equals(one)){
				ans = ans.multiply(x).mod(m);
				y = y.subtract(one);
			}
			else{
				x = x.multiply(x).mod(m);
				y = y.divide(two);
			}
		}
		return ans;
	}
	static BigInteger power(BigInteger x, BigInteger y, BigInteger m)
	{
	    if (y.equals(0))
	        return (new BigInteger("1"));
	    BigInteger p = power(x, y.divide(new BigInteger("2")), m).mod(m);
	    p = (p.multiply(p)).mod(m);
	 
	    return (y.mod(new BigInteger("2")).equals(0))? p : (p.multiply(x)).mod(m);
	}
	static long d,x,y;
	public static void extendedEuclidian(long a, long b){
		if(b == 0) {
	        d = a;
	        x = 1;
	        y = 0;
	    }
	    else {
	        extendedEuclidian(b, a%b);
	        int temp = (int) x;
	        x = y;
	        y = temp - (a/b)*y;
	    }
	}
	
	public static long gcd(long n, long m){
		if(m!=0) return gcd(m,n%m);
		else return n;
	}
	
	
	public static class FasterScanner {
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
 
		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = System.in.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
 
		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}
 
		public String nextString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}
 
		public long nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long 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 int nextInt() {
			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 int[] nextIntArray(int n) {
	        return nextIntArray(n, 0);
	    }
	    
	    public int[] nextIntArray(int n, int off) {
	    	int[] arr = new int[n + off];
	    	for (int i = 0; i < n; i++) {
	    		arr[i + off] = nextInt();
	    	}
	    	return arr;
	    }
	    
	    public long[] nextLongArray(int n) {
	    	return nextLongArray(n, 0);
	    }
        
		public long[] nextLongArray(int n, int off) {
		    long[] arr = new long[n + off];
		    for (int i = 0; i < n; i++) {
		        arr[i + off] = nextLong();
		    }
		    return arr;
		}
 
	    private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
 
		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
	}
}