A New Year party is not a New Year party without lemonade! As usual, you are expecting a lot of guests, and buying lemonade has already become a pleasant necessity.

Your favorite store sells lemonade in bottles of n different volumes at different costs. A single bottle of type i has volume 2i - 1 liters and costs ci roubles. The number of bottles of each type in the store can be considered infinite.

You want to buy at least L liters of lemonade. How many roubles do you have to spend?

Input

The first line contains two integers n and L (1 ≤ n ≤ 30; 1 ≤ L ≤ 109) — the number of types of bottles in the store and the required amount of lemonade in liters, respectively.

The second line contains n integers c1, c2, ..., cn (1 ≤ ci ≤ 109) — the costs of bottles of different types.

Output

Output a single integer — the smallest number of roubles you have to pay in order to buy at least L liters of lemonade.

Examples

Input

4 12
20 30 70 90


Output

150


Input

4 3
10000 1000 100 10


Output

10


Input

4 3
10 100 1000 10000


Output

30


Input

5 787787787
123456789 234567890 345678901 456789012 987654321


Output

44981600785557577

Note

In the first example you should buy one 8-liter bottle for 90 roubles and two 2-liter bottles for 30 roubles each. In total you'll get 12 liters of lemonade for just 150 roubles.

In the second example, even though you need only 3 liters, it's cheaper to buy a single 8-liter bottle for 10 roubles.

In the third example it's best to buy three 1-liter bottles for 10 roubles each, getting three liters for 30 roubles.
import java.util.*;
import java.io.*;

public class ProbC implements Runnable{

	private static InputStream stream;
	private static byte[] buf = new byte[1024];
	private static int curChar;
	private static int numChars;
	private static SpaceCharFilter filter;
	private static PrintWriter pw;
	

	private static void soln(){
		int n = nextInt(), l = nextInt(),c[] = new int[n];
		c = nextIntArray(n);
		for (int i=0; i<n-1; i++) {
			c[i+1] = Math.min(c[i+1],2*c[i]); 
		}
		long ans = (long)4e18;
		long sum = 0;
		for (int i = n-1; i>=0; i--) {
			int need = l/(1<<i);
			sum += (long) need * c[i];
			l -= (long)need << i;
			if(l>0)
				ans = Math.min(ans, sum +c[i]);
			else
				ans = Math.min(ans,sum);
//	    	System.out.println(ans);
		}
		System.out.println(ans);
	}

	public void run (){
		soln();
	}

	public static void main(String[] args) throws InterruptedException{
		InputReader(System.in);
		pw = new PrintWriter(System.out);
		Thread t = new Thread(null, new ProbC(), "ProbC", 1<<28);
		t.start();
		t.join();
		pw.close();
	}


	// To Get Input
	// Some Buffer Methods

	public static void InputReader(InputStream stream1) {
		stream = stream1;
	}

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

	private static boolean isEndOfLine(int c) {
		return c == '\n' || c == '\r' || c == -1;
	}

	private static 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++];
	}

	private static 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;
	}
 
	private static 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;
	}
 
	private static String nextToken() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}
 
	private static 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();
	}

	private static int[] nextIntArray(int n) {
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nextInt();
		}
		return arr;
	}
	  
	private static long[] nextLongArray(int n) {
		long[] arr = new long[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nextLong();
		}
		return arr;
	}

	private static void pArray(int[] arr){
		for (int i=0; i<arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private static void pArray(long[] arr){
		for (int i=0; i<arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;		
	}

	private static boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}
 
	private interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}

}