There are N cities in Republic of AtCoder. The size of the i-th city is A_{i}. Takahashi would like to build N-1 bidirectional roads connecting two cities so that any city can be reached from any other city by using these roads.

Assume that the cost of building a road connecting the i-th city and the j-th city is |i-j| \times D + A_{i} + A_{j}. For Takahashi, find the minimum possible total cost to achieve the objective.

Constraints

* 1 \leq N \leq 2 \times 10^5
* 1 \leq D \leq 10^9
* 1 \leq A_{i} \leq 10^9
* A_{i} and D are integers.

Input

Input is given from Standard Input in the following format:


N D
A_1 A_2 ... A_N


Output

Print the minimum possible total cost.

Examples

Input

3 1
1 100 1


Output

106


Input

3 1000
1 100 1


Output

2202


Input

6 14
25 171 7 1 17 162


Output

497


Input

12 5
43 94 27 3 69 99 56 25 8 15 46 8


Output

658
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		MyInput in = new MyInput(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		EConnectingCities solver = new EConnectingCities();
		solver.solve(1, in, out);
		out.close();
	}

	static class EConnectingCities {
		public void solve(int testNumber, MyInput in, PrintWriter out) {
			int n = in.nextInt();
			long d = in.nextLong();
			long[] a = in.nextLongArray(n);

			UnionFind uf = new UnionFind(n);
			long ans = 0;

			while (uf.size(0) != n) {
				long[] val = new long[n + 2];
				long[] val2 = new long[n + 2];
				long[] valL = new long[n + 2];
				long[] valR = new long[n + 2];
				Arrays.fill(valL, Long.MAX_VALUE / 2);
				Arrays.fill(valR, Long.MAX_VALUE / 2);
				Arrays.fill(val, Long.MAX_VALUE / 2);
				Arrays.fill(val2, Long.MAX_VALUE / 2);
				int[] indexL = new int[n + 2];
				int[] indexR = new int[n + 2];
				for (int i = 0; i < n; i++) {
					if (valL[uf.root(i) + 1] > a[i] - i * d) {
						valL[uf.root(i) + 1] = a[i] - i * d;
						indexL[uf.root(i) + 1] = i;
					}
					if (valR[uf.root(i) + 1] > a[i] + i * d) {
						valR[uf.root(i) + 1] = a[i] + i * d;
						indexR[uf.root(i) + 1] = i;
					}
					val[uf.root(i) + 1] = Math.min(val[uf.root(i) + 1], a[i] + i * d);
					val2[uf.root(i) + 1] = Math.min(val2[uf.root(i) + 1], a[i] - i * d);
				}

				int[] minL = new int[n + 2];
				int[] minR = new int[n + 2];

				for (int i = 1; i <= n; i++) {
					minL[i] = valL[minL[i - 1]] >= valL[i] ? i : minL[i - 1];
				}

				minR[n + 1] = n + 1;
				for (int i = n; i >= 1; i--) {
					minR[i] = valR[minR[i + 1]] >= valR[i] ? i : minR[i + 1];
				}

				for (int i = 1; i <= n; i++) {
					if (uf.root(i - 1) != i - 1)
						continue;
					long cl = valL[minL[i - 1]] + val[i];
					long cr = valR[minR[i + 1]] + val2[i];
					//                dump(i, cl, cr);
					if (cl <= cr) {
						if (!uf.same(i - 1, minL[i - 1] - 1)) {
							ans += cl;
							uf.union(i - 1, minL[i - 1] - 1);
						}
					} else {
						//                    dump(i, cl, cr, valR, minR, val2);
						//                    dump(i, cl, cr, minL, valL, val);
						if (!uf.same(i - 1, minR[i + 1] - 1)) {
							ans += cr;
							uf.union(i - 1, minR[i + 1] - 1);
						}

					}
				}
			}
			out.println(ans);
		}

	}

	static class MyInput {
		private final BufferedReader in;
		private static int pos;
		private static int readLen;
		private static final char[] buffer = new char[1024 * 8];
		private static char[] str = new char[500 * 8 * 2];
		private static boolean[] isDigit = new boolean[256];
		private static boolean[] isSpace = new boolean[256];
		private static boolean[] isLineSep = new boolean[256];

		static {
			for (int i = 0; i < 10; i++) {
				isDigit['0' + i] = true;
			}
			isDigit['-'] = true;
			isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
			isLineSep['\r'] = isLineSep['\n'] = true;
		}

		public MyInput(InputStream is) {
			in = new BufferedReader(new InputStreamReader(is));
		}

		public int read() {
			if (pos >= readLen) {
				pos = 0;
				try {
					readLen = in.read(buffer);
				} catch (IOException e) {
					throw new RuntimeException();
				}
				if (readLen <= 0) {
					throw new MyInput.EndOfFileRuntimeException();
				}
			}
			return buffer[pos++];
		}

		public int nextInt() {
			int len = 0;
			str[len++] = nextChar();
			len = reads(len, isSpace);
			int i = 0;
			int ret = 0;
			if (str[0] == '-') {
				i = 1;
			}
			for (; i < len; i++)
				ret = ret * 10 + str[i] - '0';
			if (str[0] == '-') {
				ret = -ret;
			}
			return ret;
		}

		public long nextLong() {
			int len = 0;
			str[len++] = nextChar();
			len = reads(len, isSpace);
			int i = 0;
			long ret = 0;
			if (str[0] == '-') {
				i = 1;
			}
			for (; i < len; i++)
				ret = ret * 10 + str[i] - '0';
			if (str[0] == '-') {
				ret = -ret;
			}
			return ret;
		}

		public char nextChar() {
			while (true) {
				final int c = read();
				if (!isSpace[c]) {
					return (char) c;
				}
			}
		}

		int reads(int len, boolean[] accept) {
			try {
				while (true) {
					final int c = read();
					if (accept[c]) {
						break;
					}
					if (str.length == len) {
						char[] rep = new char[str.length * 3 / 2];
						System.arraycopy(str, 0, rep, 0, str.length);
						str = rep;
					}
					str[len++] = (char) c;
				}
			} catch (MyInput.EndOfFileRuntimeException e) {
			}
			return len;
		}

		public long[] nextLongArray(final int n) {
			final long[] res = new long[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextLong();
			}
			return res;
		}

		static class EndOfFileRuntimeException extends RuntimeException {
		}

	}
}

/**
 * Union-Find木
 * @author Yuichiro.Yamashita
 *
 */
class UnionFind {

	private int[] data;

	/**
	 * コンストラクタ
	 * @param size
	 */
	public UnionFind(final int size) {
		data = new int[size];
		clear();
	}

	/**
	 * 全てのデータを初期化
	 */
	public void clear() {
		Arrays.fill(data, -1);
	}

	public int root(final int x) {
		if (data[x] < 0) {
			return x;
		} else {
			return root(data[x]);
		}
	}

	public void union(int x, int y) {
		if ((x = root(x)) != (y = root(y))) {
			if (data[y] < data[x]) {
				final int t = x;
				x = y;
				y = t;
			}
			data[x] += data[y];
			data[y] = x;
		}
	}

	public boolean same(int x, int y) {
		return root(x) == root(y);
	}

	public int size(int x) {
		return -data[root(x)];
	}

}
