There are several days left before the fiftieth birthday of a famous Berland's writer Berlbury. In this connection the local library decided to make an exposition of the works of this famous science-fiction writer. It was decided as well that it is necessary to include into the exposition only those books that were published during a particular time period. It is obvious that if the books differ much in size, the visitors will not like it. That was why the organizers came to the opinion, that the difference between the highest and the lowest books in the exposition should be not more than k millimeters.

The library has n volumes of books by Berlbury, arranged in chronological order of their appearance. The height of each book in millimeters is know, it is hi. As Berlbury is highly respected in the city, the organizers want to include into the exposition as many books as possible, and to find out what periods of his creative work they will manage to cover. You are asked to help the organizers cope with this hard task.

Input

The first line of the input data contains two integer numbers separated by a space n (1 ≤ n ≤ 105) and k (0 ≤ k ≤ 106) — the amount of books by Berlbury in the library, and the maximum allowed height difference between the lowest and the highest books. The second line contains n integer numbers separated by a space. Each number hi (1 ≤ hi ≤ 106) is the height of the i-th book in millimeters.

Output

In the first line of the output data print two numbers a and b (separate them by a space), where a is the maximum amount of books the organizers can include into the exposition, and b — the amount of the time periods, during which Berlbury published a books, and the height difference between the lowest and the highest among these books is not more than k milllimeters.

In each of the following b lines print two integer numbers separated by a space — indexes of the first and the last volumes from each of the required time periods of Berlbury's creative work.

Examples

Input

3 3
14 12 10


Output

2 2
1 2
2 3


Input

2 0
10 10


Output

2 1
1 2


Input

4 5
8 19 10 13


Output

2 1
3 4
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.util.*;

/**
 * 6E
 *
 * @author artyom
 */
public class Exposition implements Runnable {
    private BufferedReader in;
    private PrintStream out;
    private StringTokenizer tok;

    private void solve() throws IOException {
        int n = nextInt() + 1, k = nextInt(), maxDist = 0;
        int[] ary = readIntArray(n);
        SegmentTreeMax segmentTreeMax = new SegmentTreeMax(ary);
        SegmentTreeMin segmentTreeMin = new SegmentTreeMin(ary);
        Collection<Pair> intervals = Collections.emptyList();
        for (int i = 1, j = 0, min = ary[0], max = ary[0], minInd = 0, maxInd = 0; i < n; i++) {
            if (ary[i] < min) {
                min = ary[i];
                minInd = i;
            }
            if (ary[i] > max) {
                max = ary[i];
                maxInd = i;
            }
            if (max - min > k) {
                if (i - j > maxDist) {
                    maxDist = i - j;
                    intervals = new LinkedList<>();
                }
                if (i - j >= maxDist) {
                    intervals.add(new Pair(j, i - 1));
                }
                while (max - min > k) {
                    if (max == ary[i]) {
                        j = minInd + 1;
                        if (j < i) {
                            Pair p = segmentTreeMin.evaluate(j, i - 1);
                            min = p.a;
                            minInd = p.b;
                        } else {
                            min = ary[j];
                            minInd = j;
                        }
                    } else {
                        j = maxInd + 1;
                        if (j < i) {
                            Pair p = segmentTreeMax.evaluate(j, i - 1);
                            max = p.a;
                            maxInd = p.b;
                        } else {
                            max = ary[j];
                            maxInd = j;
                        }
                    }
                }
            }
        }
        StringBuilder sb = new StringBuilder();
        sb.append(maxDist).append(" ").append(intervals.size()).append('\n');
        for (Pair interval : intervals) {
            sb.append(interval.a + 1).append(" ").append(interval.b + 1).append('\n');
        }
        out.print(sb);
    }

    //--------------------------------------------------------------
    public static void main(String[] args) {
        new Exposition().run();
    }

    @Override
    public void run() {
        try {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = System.out;
            tok = null;
            solve();
            in.close();
        } catch (IOException e) {
            System.exit(0);
        }
    }

    private String nextToken() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }

    private int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    private int[] readIntArray(int n) throws IOException {
        int m = n - 1;
        int[] arr = new int[n];
        for (int i = 0; i < m; i++) {
            arr[i] = nextInt();
        }
        arr[m] = Integer.MAX_VALUE - 1;
        return arr;
    }

    static final class SegmentTreeMin {
        private final Pair[] st;
        private final int arrSize;

        SegmentTreeMin(int[] arr) {
            st = new Pair[getMaxSize(arrSize = arr.length)];

            build(arr, 0, arrSize - 1, 0);
        }

        private static int getMaxSize(int arrSize1) {
            int x = (int) Math.ceil(Math.log10(arrSize1) / Math.log10(2));
            return 2 * (int) Math.pow(2, x) - 1;
        }

        private Pair build(int[] arr, int ss, int se, int si) {
            if (ss == se) {
                return st[si] = new Pair(arr[ss], ss);
            }

            int mid = getMid(ss, se);
            st[si] = min(build(arr, ss, mid, si * 2 + 1),
                    build(arr, mid + 1, se, si * 2 + 2));
            return st[si];
        }

        private static Pair min(Pair p, Pair q) {
            return p.compareTo(q) < 0 ? p : q;
        }

        private static int getMid(int s, int e) {
            return s + (e - s) / 2;
        }

        Pair evaluate(int qs, int qe) {
            return evaluate(0, arrSize - 1, qs, qe, 0);
        }

        private Pair evaluate(int ss, int se, int qs, int qe, int index) {
            if (qs <= ss && qe >= se) {
                return st[index];
            }

            if (se < qs || ss > qe) {
                return new Pair(Integer.MAX_VALUE, index);
            }

            int mid = getMid(ss, se);
            return min(evaluate(ss, mid, qs, qe, 2 * index + 1),
                    evaluate(mid + 1, se, qs, qe, 2 * index + 2));
        }
    }

    static final class SegmentTreeMax {
        private final Pair[] st;
        private final int arrSize;

        SegmentTreeMax(int[] arr) {
            st = new Pair[getMaxSize(arrSize = arr.length)];

            build(arr, 0, arrSize - 1, 0);
        }

        private static int getMaxSize(int arrSize1) {
            int x = (int) Math.ceil(Math.log10(arrSize1) / Math.log10(2));
            return 2 * (int) Math.pow(2, x) - 1;
        }

        private Pair build(int[] arr, int ss, int se, int si) {
            if (ss == se) {
                return st[si] = new Pair(arr[ss], ss);
            }

            int mid = getMid(ss, se);
            st[si] = max(build(arr, ss, mid, si * 2 + 1),
                    build(arr, mid + 1, se, si * 2 + 2));
            return st[si];
        }

        private static Pair max(Pair p, Pair q) {
            return p.compareTo(q) > 0 ? p : q;
        }

        private static int getMid(int s, int e) {
            return s + (e - s) / 2;
        }

        Pair evaluate(int qs, int qe) {
            return evaluate(0, arrSize - 1, qs, qe, 0);
        }

        private Pair evaluate(int ss, int se, int qs, int qe, int index) {
            if (qs <= ss && qe >= se) {
                return st[index];
            }

            if (se < qs || ss > qe) {
                return new Pair(Integer.MIN_VALUE, index);
            }

            int mid = getMid(ss, se);
            return max(evaluate(ss, mid, qs, qe, 2 * index + 1),
                    evaluate(mid + 1, se, qs, qe, 2 * index + 2));
        }
    }

    private static final class Pair implements Comparable<Pair> {
        int a;
        int b;

        Pair(int a, int b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public int compareTo(Pair that) {
            return Integer.compare(a, that.a);
        }
    }
}