We all know the impressive story of Robin Hood. Robin Hood uses his archery skills and his wits to steal the money from rich, and return it to the poor.

There are n citizens in Kekoland, each person has ci coins. Each day, Robin Hood will take exactly 1 coin from the richest person in the city and he will give it to the poorest person (poorest person right after taking richest's 1 coin). In case the choice is not unique, he will select one among them at random. Sadly, Robin Hood is old and want to retire in k days. He decided to spend these last days with helping poor people. 

After taking his money are taken by Robin Hood richest person may become poorest person as well, and it might even happen that Robin Hood will give his money back. For example if all people have same number of coins, then next day they will have same number of coins too. 

Your task is to find the difference between richest and poorest persons wealth after k days. Note that the choosing at random among richest and poorest doesn't affect the answer.

Input

The first line of the input contains two integers n and k (1 ≤ n ≤ 500 000, 0 ≤ k ≤ 109) — the number of citizens in Kekoland and the number of days left till Robin Hood's retirement.

The second line contains n integers, the i-th of them is ci (1 ≤ ci ≤ 109) — initial wealth of the i-th person.

Output

Print a single line containing the difference between richest and poorest peoples wealth.

Examples

Input

4 1
1 1 4 2


Output

2


Input

3 1
2 2 2


Output

0

Note

Lets look at how wealth changes through day in the first sample.

  1. [1, 1, 4, 2]
  2. [2, 1, 3, 2] or [1, 2, 3, 2]



So the answer is 3 - 1 = 2

In second sample wealth will remain the same for each person.
import java.io.*;
import java.math.*;
import java.util.*;

public class Main {

	static int mod = (int) 1e9 + 7;
	static int MAX = (int) 1e9;
	static ArrayList<Integer>[] g;
	static int n, m;
	static long k;
	static int[][] a;
	static int nodes = 0;
	static int edges = 0;
	static boolean[][] done;
	static int[][] ans;
	static int[] dp;
	static int curX, curY;
	static int rx, ry, x1, y1, x2, y2;

	public static void main(String[] args) {
		FasterScanner s = new FasterScanner();
		PrintWriter out = new PrintWriter(System.out);
		int test = 1;
		testloop: while (test-- > 0) {
			int n = s.nextInt();
			int k = s.nextInt();
			int[] a = s.nextIntArray(n);
			long[] postSum = new long[n + 1];

			Arrays.sort(a);
			postSum[n - 1] = a[n - 1];
			for (int i = n - 2; i >= 0; i--)
				postSum[i] = a[i] + postSum[i + 1];
			long[] presum = new long[n + 1];
			presum[1] = a[0];
			for (int i = 2; i <= n; i++)
				presum[i] = a[i-1] + presum[i - 1];

			int left = 0;
			int right = (int) 1e9;
			while (left < right) {
				int mid = (left + right) / 2;
				int pos = find(a, mid);
				long total = postSum[pos] - (long)(n - pos) * mid;
				if (total > k) {
					left = mid + 1;
				} else {
					right = mid;
				}
			}
			int finalMax = right;
			left = 0;
			right = (int) 1e9;
			while (left < right) {
				int mid = (left + right + 1) / 2;
				int pos = find(a, mid) ;
				long total = (long)(pos ) * mid - presum[pos];
//				System.out.println("HERE "+ left+" "+right +" "+mid);
				if (total > k) {
					right = mid - 1;
				} else {
					left = mid;
				}
			}
			int finalMin = right;
//			System.out.println(finalMax +" "+finalMin);
//			System.out.println(Math.max(finalMax - finalMin,0));
			int answer = finalMax - finalMin;
			if(finalMax <= finalMin)
			{
				long total = postSum[0];
				if(total % n == 0)
					answer = 0;
				else
					answer = 1;
			}
			System.out.println(answer);
		}

		out.close();
	}	

	public static int find(int[] a, int val) {
		int left = 0;
		if (val > a[a.length - 1])
			return a.length;
		int right = a.length;

		while (left < right) {
			
			int mid = (left + right) >> 1;
//			System.out.println("HERE" + left +" " + right +" "+mid);
		
			if (a[mid] > val) {
				right = mid;
			} else {
				left = mid + 1;
			}
		}
		return right;
	}

	static class Pair implements Comparable<Pair> {
		long x;
		long y;

		public int compareTo(Pair o) {
			return Double.compare(this.curDistance(), o.curDistance());
		}

		public double curDistance() {
			return Math.sqrt((x - curX) * (x - curX) + (y - curY) * (y - curY))
					- Math.sqrt((x - rx) * (x - rx) + (y - ry) * (y - ry));
		}

		public double distance1() {
			return Math.sqrt((x - x1) * (x - x1) + (y - y1) * (y - y1))
					- Math.sqrt((x - rx) * (x - rx) + (y - ry) * (y - ry));
		}

		public double distance2() {
			return Math.sqrt((x - x2) * (x - x2) + (y - y2) * (y - y2))
					- Math.sqrt((x - rx) * (x - rx) + (y - ry) * (y - ry));
		}

		public double distance() {
			return 2 * Math.sqrt((x - rx) * (x - rx) + (y - ry) * (y - ry));
		}
	}

	static class Component implements Comparable<Component> {
		int id;
		int size;

		Component(int id, int size) {
			this.id = id;
			this.size = size;
		}

		@Override
		public int compareTo(Component o) {
			return size - o.size;
		}
	}

	static class Point {
		int x, y;

		Point(int xx, int yy) {
			x = xx;
			y = yy;
		}
	}

	static void dfs(int x, int y, int rem, int val) {
		if (rem <= 0)
			return;
		rem--;
		done[x][y] = true;
		if (check(x + 1, y) && !done[x + 1][y] && a[x + 1][y] >= val)
			dfs(x + 1, y, rem, val);
		if (check(x - 1, y) && !done[x - 1][y] && a[x - 1][y] >= val)
			dfs(x - 1, y, rem, val);
		if (check(x, y + 1) && !done[x][y + 1] && a[x][y + 1] >= val)
			dfs(x, y + 1, rem, val);
		if (check(x, y - 1) && !done[x][y - 1] && a[x][y - 1] >= val)
			dfs(x, y - 1, rem, val);
	}

	static boolean check(int x, int y) {
		return x >= 0 && y >= 0 && x < n && y < m;
	}

	static class Player implements Comparable<Player> {
		String name;
		int score;

		Player(String n, int v) {
			name = n;
			score = v;
		}

		@Override
		public int compareTo(Player o) {
			return o.score - score;
		}
	}

	static class Edge {
		int t, rev, f;
		long cap;

		public Edge(int t, int rev, long cap) {
			this.t = t;
			this.rev = rev;
			this.cap = cap;
		}
	}

	public static List<Edge>[] createGraph(int nodes) {
		List<Edge>[] graph = new List[nodes];
		for (int i = 0; i < nodes; i++)
			graph[i] = new ArrayList<>();
		return graph;
	}

	public static void addEdge(List<Edge>[] graph, int s, int t, long cap) {
		graph[s].add(new Edge(t, graph[t].size(), cap));
		graph[t].add(new Edge(s, graph[s].size() - 1, 0));
	}

	static boolean dinicBfs(List<Edge>[] graph, int src, int dest, int[] dist) {
		Arrays.fill(dist, -1);
		dist[src] = 0;
		int[] Q = new int[graph.length];
		int sizeQ = 0;
		Q[sizeQ++] = src;
		for (int i = 0; i < sizeQ; i++) {
			int u = Q[i];
			for (Edge e : graph[u]) {
				if (dist[e.t] < 0 && e.f < e.cap) {
					dist[e.t] = dist[u] + 1;
					Q[sizeQ++] = e.t;
				}
			}
		}
		return dist[dest] >= 0;
	}

	static long dinicDfs(List<Edge>[] graph, int[] ptr, int[] dist, int dest, int u, long l) {
		if (u == dest)
			return l;
		for (; ptr[u] < graph[u].size(); ++ptr[u]) {
			Edge e = graph[u].get(ptr[u]);
			if (dist[e.t] == dist[u] + 1 && e.f < e.cap) {
				long df = dinicDfs(graph, ptr, dist, dest, e.t, Math.min(l, e.cap - e.f));
				if (df > 0) {
					e.f += df;
					graph[e.t].get(e.rev).f -= df;
					return df;
				}
			}
		}
		return 0;
	}

	public static long maxFlow(List<Edge>[] graph, int src, int dest) {
		long flow = 0;
		int[] dist = new int[graph.length];
		while (dinicBfs(graph, src, dest, dist)) {
			int[] ptr = new int[graph.length];
			while (true) {
				long df = dinicDfs(graph, ptr, dist, dest, src, Integer.MAX_VALUE);
				if (df == 0)
					break;
				flow += df;
			}
		}
		return flow;
	}

	static int ans(ArrayList<Character>[] l, char a, int n) {
		if (n == 1)
			return 1;
		int sum = 0;
		for (int i = 0; i < l[a - 'a'].size(); i++) {
			sum += ans(l, l[a - 'a'].get(i), n - 1);
		}
		return sum;
	}

	static void dfs1(List<Integer>[] graph, boolean[] used, List<Integer> order, int u) {
		used[u] = true;
		for (int v : graph[u])
			if (!used[v])
				dfs1(graph, used, order, v);
		order.add(u);
	}

	static void dfs2(List<Integer>[] reverseGraph, int[] comp, int u, int color) {
		comp[u] = color;
		for (int v : reverseGraph[u])
			if (comp[v] == -1)
				dfs2(reverseGraph, comp, v, color);
	}

	public static boolean[] solve2Sat(List<Integer>[] graph) {
		int n = graph.length;
		boolean[] used = new boolean[n];
		List<Integer> order = new ArrayList<>();
		for (int i = 0; i < n; ++i)
			if (!used[i])
				dfs1(graph, used, order, i);

		List<Integer>[] reverseGraph = new List[n];
		for (int i = 0; i < n; i++)
			reverseGraph[i] = new ArrayList<>();
		for (int i = 0; i < n; i++)
			for (int j : graph[i])
				reverseGraph[j].add(i);

		int[] comp = new int[n];
		Arrays.fill(comp, -1);
		for (int i = 0, color = 0; i < n; ++i) {
			int u = order.get(n - i - 1);
			if (comp[u] == -1)
				dfs2(reverseGraph, comp, u, color++);
		}

		for (int i = 0; i < n; ++i)
			if (comp[i] == comp[i ^ 1])
				return null;

		boolean[] res = new boolean[n / 2];
		for (int i = 0; i < n; i += 2)
			res[i / 2] = comp[i] > comp[i ^ 1];
		return res;
	}

	public static int[] createSets(int size) {
		int[] p = new int[size];
		for (int i = 0; i < size; i++)
			p[i] = i;
		return p;
	}

	public static int root(int[] p, int x) {
		return x == p[x] ? x : (p[x] = root(p, p[x]));
	}

	public static void unite(int[] p, int a, int b) {
		a = root(p, a);
		b = root(p, b);
		if (a != b)
			p[a] = b;
	}

	public static boolean nextPermutation(int[] p) {
		for (int a = p.length - 2; a >= 0; --a)
			if (p[a] < p[a + 1])
				for (int b = p.length - 1;; --b)
					if (p[b] > p[a]) {
						int t = p[a];
						p[a] = p[b];
						p[b] = t;
						for (++a, b = p.length - 1; a < b; ++a, --b) {
							t = p[a];
							p[a] = p[b];
							p[b] = t;
						}
						return true;
					}
		return false;
	}

	public static boolean isPrime(long n) {
		if (n <= 1)
			return false;
		for (long i = 2; i * i <= n; i++)
			if (n % i == 0)
				return false;
		return true;
	}

	static class SegTree {
		int[] val;
		int n;

		SegTree(int n) {
			val = new int[2 * n];
			this.n = n;
		}

		void upd(int p, int l) {
			p += n;
			val[p] = l;
			for (; (p >>= 1) != 0;) {
				val[p] = Math.max(val[2 * p], val[2 * p + 1]);

			}
		}

		int query(int l, int r) { // sum on interval [l, r)
			// System.out.println(l+" "+r);
			int res = 0;
			for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
				if ((l & 1) != 0)
					res = Math.max(res, val[l++]);
				if ((r & 1) != 0)
					res = Math.max(res, val[--r]);
			}
			return res;
		}
	}

	static boolean check(int i, int j, int n) {
		if (i >= 0 && j >= 0 && i < n && j < n)
			return true;
		return false;
	}

	public static int[] generateDivisorTable(int n) {
		int[] divisor = new int[n + 1];
		for (int i = 1; i <= n; i++)
			divisor[i] = i;
		for (int i = 2; i * i <= n; i++)
			if (divisor[i] == i)
				for (int j = i * i; j <= n; j += i)
					divisor[j] = i;
		return divisor;
	}

	public static int[][] matrixMul(int[][] a, int[][] b) {
		int n = a.length;
		int m = a[0].length;
		int k = b[0].length;
		int[][] res = new int[n][k];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < k; j++) {
				for (int p = 0; p < m; p++) {
					res[i][j] = (res[i][j] + (int) ((a[i][p] * 1l * b[p][j]) % mod)) % mod;
				}
			}
		}
		return res;
	}

	public static int[][] matrixPow(int[][] a, int p) {
		if (p == 0) {
			return matrixUnit(a.length);
		} else if (p % 2 == 0) {
			return matrixPow(matrixMul(a, a), p / 2);
		} else {
			return matrixMul(a, matrixPow(a, p - 1));
		}
	}

	public static int[][] matrixUnit(int n) {
		int[][] res = new int[n][n];
		for (int i = 0; i < n; ++i) {
			res[i][i] = 1;
		}
		return res;
	}

	static int[] modInv(int n, int mod) {
		int[] ans = new int[n];
		for (int i = 1; i < n; i++)
			ans[i] = (int) pow(i, mod - 2, mod);
		return ans;
	}

	static int[] primes;

	public static long ncr(int n, int r) {
		if (n < r)
			return 0;
		if (n == r)
			return 1;
		if (r == 0)
			return 1;
		if (r < 0)
			return 0;
		long ans = 1;
		for (int i = 0; i < primes.length; i++) {
			long power = count(n, primes[i]) - count(n - r, primes[i]) - count(r, primes[i]);
			ans *= pow(primes[i], power, mod);
			ans %= mod;
		}
		return ans;
	}

	public static long pow(long x, long n, int mod) {
		long res = 1;
		for (long p = x; n > 0; n >>= 1, p = (p * p) % mod) {
			if ((n & 1) != 0) {
				res = (int) (res * p % mod);
			}
		}
		return res;
	}

	public static long count(int n, int p) {
		long count = 0;
		long z = p;
		while (z <= n) {
			count += n / z;
			z *= p;
		}
		return count;

	}

	public static int[] generatePrimes(int n) {
		boolean[] prime = new boolean[n + 1];
		Arrays.fill(prime, 2, n + 1, true);
		for (int i = 2; i * i <= n; i++)
			if (prime[i])
				for (int j = i * i; j <= n; j += i)
					prime[j] = false;
		int[] primes = new int[n + 1];
		int cnt = 0;
		for (int i = 0; i < prime.length; i++)
			if (prime[i])
				primes[cnt++] = i;

		return Arrays.copyOf(primes, cnt);
	}

	static class Pairxy implements Comparable<Pairxy> {
		int x;
		int y;

		Pairxy(int x, int y) {
			this.x = x;
			this.y = y;
		}

		public int compareTo(Pairxy o) {
			return Integer.compare(this.x, o.x);
		}

	}

	public static long C(int n, int r) {
		long ans = 1;
		int x = 1;
		while (x <= r) {
			ans *= n;
			ans /= x;
			x++;
			n--;
		}
		return ans;
	}

	static class DisjointSetsRank {

		int[] p;
		int[] rank;
		int[] size;

		public DisjointSetsRank(int size) {
			p = new int[size];
			this.size = new int[size];
			for (int i = 0; i < size; i++) {
				p[i] = i;
				this.size[i] = 1;
			}
			rank = new int[size];
		}

		public int root(int x) {
			return x == p[x] ? x : (p[x] = root(p[x]));
		}

		public int sameSet(int x, int y) {
			if (root(x) == root(y))
				return 1;
			return 0;

		}

		public int unite(int a, int b) {
			a = root(a);
			b = root(b);
			if (a == b)
				return -1;

			if (rank[a] < rank[b]) {
				p[a] = b;
				size[b] += size[a];
				return a;
			} else {
				p[b] = a;
				size[a] += size[b];
				if (rank[a] == rank[b])
					++rank[a];
				return b;
			}
		}

	}

	static int gcd(long m, long n) {
		long x;
		long y;
		while (m % n != 0) {
			x = n;
			y = m % n;
			m = x;
			n = y;
		}
		return (int) n;
	}

	static class FasterScanner {
		private byte[] buf = new byte[1024];
		private int curChar;
		private int snumChars;

		public int read() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = System.in.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 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) {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n) {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = 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;
		}
	}
}