The only difference between the easy and the hard versions is the maximum value of k.

You are given an infinite sequence of form "112123123412345..." which consist of blocks of all consecutive positive integers written one after another. The first block consists of all numbers from 1 to 1, the second one — from 1 to 2, the third one — from 1 to 3, ..., the i-th block consists of all numbers from 1 to i. 

So the first 56 elements of the sequence are "11212312341234512345612345671234567812345678912345678910". Elements of the sequence are numbered from one. For example, the 1-st element of the sequence is 1, the 3-rd element of the sequence is 2, the 20-th element of the sequence is 5, the 38-th element is 2, the 56-th element of the sequence is 0.

Your task is to answer q independent queries. In the i-th query you are given one integer k_i. Calculate the digit at the position k_i of the sequence.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 500) — the number of queries.

The i-th of the following q lines contains one integer k_i (1 ≤ k_i ≤ 10^9) — the description of the corresponding query.

Output

Print q lines. In the i-th line print one digit x_i (0 ≤ x_i ≤ 9) — the answer to the query i, i.e. x_i should be equal to the element at the position k_i of the sequence.

Examples

Input


5
1
3
20
38
56


Output


1
2
5
2
0


Input


4
2132
506
999999999
1000000000


Output


8
2
9
8

Note

Answers on queries from the first example are described in the problem statement.
import java.io.*;
import java.util.*;
 
 
 
public class Main {
	
	static InputReader in = new InputReader(System.in);
	static PrintWriter out = new PrintWriter(System.out);
	
	static int oo = (int)1e9;
	static int mod = 1000000007;
	
	static int[] di = {-1, 1, 0, 0};
	static int[] dj = {0, 0, -1, 1};
	
	
	public static void main(String[] args) throws IOException {
 
		int q = in.nextInt();
		while(q --> 0) {
			long k = in.nextLong();
			long l = 1, r = 1000000000;
			long x = -1;
			long M = -1;
			while(l <= r) {
				long mid = (l + r) / 2;
				long n = need(mid);
				if(n <= k) {
					x = n;
					M = mid;
					l = mid + 1;
				}
				else {
					r = mid - 1;
				}
			}
			long ans = x == k ? M % 10 : digit( k - x );
			System.out.println(ans);
		}
		
		
		out.close();
	}
	
	static long need(long k) {
		long ret = 0;
		long d = 1;
		long m = 1, M = 10;
		while(k >= m) {
			long max = Math.min(k, M-1);
			long n = max - m + 1;
			long a = k - m + 1, b = k - max + 1;
			ret += (a + b) * n / 2 * d;
			d ++;
			m *= 10; M *= 10;
		}
		return ret;
	}
	
	static long need2(long k) {
		long ret = 0;
		for(long i = 1; i <= k; ++i) {
			long x = i;
			while(x > 0) {
				ret++;
				x /= 10;
			}
		}
		return ret;
	}
	
	static long digit(long k) {
		int i = 1;
		for(long n = 1; ; ++n) {
			long x = n;
			ArrayDeque<Long> dq = new ArrayDeque<>();
			while(x > 0) {
				dq.addFirst(x % 10);
				x /= 10;
			}
			while(!dq.isEmpty()) {
				if(i == k)
					return dq.peek();
				dq.poll();
				i++;
			}
		}
	}
	
	static class SegmentTree {
		int n;
		long[] a, seg;
		int DEFAULT_VALUE = 0;
		
		public SegmentTree(long[] a, int n) {
			super();
			this.a = a;
			this.n = n;
			seg = new long[n * 4 + 1];
			build(1, 0, n-1);
		}
		
		private long build(int node, int i, int j) {
			if(i == j)
				return seg[node] = a[i];
			long first = build(node * 2, i, (i+j) / 2);
			long second = build(node * 2 + 1, (i+j) / 2 + 1, j);
			return seg[node] = combine(first, second);
		}
		
		long update(int k, long value) {
			return update(1, 0, n-1, k, value);
		}
		
		private long update(int node, int i, int j, int k, long value) {
			if(k < i || k > j)
				return seg[node];
			if(i == j && j == k) {
				a[k] = value;
				seg[node] = value;
				return value;
			}
			
			int m = (i + j) / 2;
			long first = update(node * 2, i, m, k, value);
			long second = update(node * 2 + 1, m + 1, j, k, value);
			return seg[node] = combine(first, second);
		}
		
		long query(int l, int r) {
			return query(1, 0, n-1, l, r);
		}
		
		private long query(int node, int i, int j, int l, int r) {
			if(l <= i && j <= r)
				return seg[node];
			if(j < l || i > r)
				return DEFAULT_VALUE;
			int m = (i + j) / 2;
			long first = query(node * 2, i, m, l, r);
			long second = query(node * 2 + 1, m+1, j, l, r);
			return combine(first, second);
		}
 
		private long combine(long a, long b) {
			return a + b;
		}
	}
	
	static class DisjointSet {
		int n;
		int[] g;
		int[] h;
		public DisjointSet(int n) {
			super();
			this.n = n;
			g = new int[n];
			h = new int[n];
			for(int i = 0; i < n; ++i) {
				g[i] = i;
				h[i] = 1;
			}
		}
		int find(int x) {
			if(g[x] == x)
				return x;
			return g[x] = find(g[x]);
		}
		void union(int x, int y) {
			x = find(x); y = find(y);
			if(x == y)
				return;
			if(h[x] >= h[y]) {
				g[y] = x;
				if(h[x] == h[y])
					h[x]++;
			}
			else {
				g[x] = y;
			}
		}
	}
	
	
	static int[] getPi(char[] a) {
		int m = a.length;
		int j = 0;
		int[] pi = new int[m];
		for(int i = 1; i < m; ++i) {
			while(j > 0 && a[i] != a[j])
				j = pi[j-1];
			if(a[i] == a[j]) {
				pi[i] = j + 1;
				j++;
			}
		}
		return pi;
	}
	
	static long lcm(long a, long b) {
		return a * b / gcd(a, b);
	}
	
	static boolean nextPermutation(int[] a) {
		for(int i = a.length - 2; i >= 0; --i) {
			if(a[i] < a[i+1]) {
				for(int j = a.length - 1; ; --j) {
					if(a[i] < a[j]) {
						int t = a[i];
						a[i] = a[j];
						a[j] = t;
						for(i++, j = a.length - 1; i < j; ++i, --j) {
							t = a[i];
							a[i] = a[j];
							a[j] = t;
						}
						return true;
					}
				}
			}
		}
		return false;
	}
	
	
	static void shuffle(int[] a) {
		Random r = new Random();
		for(int i = a.length - 1; i > 0; --i) {
			int si = r.nextInt(i);
			int t = a[si];
			a[si] = a[i];
			a[i] = t;
		}
	}
	
	static void shuffle(long[] a) {
		Random r = new Random();
		for(int i = a.length - 1; i > 0; --i) {
			int si = r.nextInt(i);
			long t = a[si];
			a[si] = a[i];
			a[i] = t;
		}
	}
	
	static int lower_bound(int[] a, int n, int k) {
		int s = 0;
		int e = n;
		int m;
		while (e - s > 0) {
			m = (s + e) / 2;
			if (a[m] < k)
				s = m + 1;
			else
				e = m;
		}
		return e;
	}
	static int lower_bound(long[] a, int n, long k) {
		int s = 0;
		int e = n;
		int m;
		while (e - s > 0) {
			m = (s + e) / 2;
			if (a[m] < k)
				s = m + 1;
			else
				e = m;
		}
		return e;
	}
	
	static int gcd(int a, int b) {
		return b == 0 ? a : gcd(b, a % b);
	}
	static long gcd(long a, long b) {
		return b == 0 ? a : gcd(b, a % b);
	}
	
	static class Pair implements Comparable<Pair> {
		int first, second;
 
		public Pair(int first, int second) {
			super();
			this.first = first;
			this.second = second;
		}
 
//		@Override
//		public int compareTo(Pair o) {
//			return this.first != o.first ? this.first - o.first : this.second - o.second;
//		}
		
		@Override
		public int compareTo(Pair o) {
			return this.first != o.first ? o.first - this.first : o.second - this.second;
		}
 
		@Override
		public int hashCode() {
			final int prime = 31;
			int result = 1;
			result = prime * result + first;
			result = prime * result + second;
			return result;
		}
 
		@Override
		public boolean equals(Object obj) {
			if (this == obj)
				return true;
			if (obj == null)
				return false;
			if (getClass() != obj.getClass())
				return false;
			Pair other = (Pair) obj;
			if (first != other.first)
				return false;
			if (second != other.second)
				return false;
			return true;
		}
	}
}
 
 
 
class InputReader {
 
	private final InputStream stream;
	private final byte[] buf = new byte[8192];
	private int curChar, snumChars;
 
	public InputReader(InputStream st) {
		this.stream = st;
	}
 
	public int read() {
		if (snumChars == -1)
			throw new InputMismatchException();
		if (curChar >= snumChars) {
			curChar = 0;
			try {
				snumChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (snumChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}
 
	public int nextInt() {
		int c = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}
 
	public long nextLong() {
		int c = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}
 
	public int[] nextIntArray(int n) {
		int a[] = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = nextInt();
		}
		return a;
	}
 
	public String readString() {
		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 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 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;
	}
 
}