Problem: The only difference between easy and hard versions is a number of elements in the array.

You are given an array a consisting of n integers. The value of the i-th element of the array is a_i.

You are also given a set of m segments. The j-th segment is [l_j; r_j], where 1 ≤ l_j ≤ r_j ≤ n.

You can choose some subset of the given set of segments and decrease values on each of the chosen segments by one (independently). For example, if the initial array a = [0, 0, 0, 0, 0] and the given segments are [1; 3] and [2; 4] then you can choose both of them and the array will become b = [-1, -2, -2, -1, 0].

You have to choose some subset of the given segments (each segment can be chosen at most once) in such a way that if you apply this subset of segments to the array a and obtain the array b then the value max_{i=1}^{n}b_i - min_{i=1}^{n}b_i will be maximum possible.

Note that you can choose the empty set.

If there are multiple answers, you can print any.

If you are Python programmer, consider using PyPy instead of Python when you submit your code.

Input

The first line of the input contains two integers n and m (1 ≤ n ≤ 10^5, 0 ≤ m ≤ 300) — the length of the array a and the number of segments, respectively.

The second line of the input contains n integers a_1, a_2, ..., a_n (-10^6 ≤ a_i ≤ 10^6), where a_i is the value of the i-th element of the array a.

The next m lines are contain two integers each. The j-th of them contains two integers l_j and r_j (1 ≤ l_j ≤ r_j ≤ n), where l_j and r_j are the ends of the j-th segment.

Output

In the first line of the output print one integer d — the maximum possible value max_{i=1}^{n}b_i - min_{i=1}^{n}b_i if b is the array obtained by applying some subset of the given segments to the array a.

In the second line of the output print one integer q (0 ≤ q ≤ m) — the number of segments you apply.

In the third line print q distinct integers c_1, c_2, ..., c_q in any order (1 ≤ c_k ≤ m) — indices of segments you apply to the array a in such a way that the value max_{i=1}^{n}b_i - min_{i=1}^{n}b_i of the obtained array b is maximum possible.

If there are multiple answers, you can print any.

Examples

Input


5 4
2 -2 3 1 2
1 3
4 5
2 5
1 3


Output


6
2
4 1 


Input


5 4
2 -2 3 1 4
3 5
3 4
2 4
2 5


Output


7
2
3 2 


Input


1 0
1000000


Output


0
0

Note

In the first example the obtained array b will be [0, -4, 1, 1, 2] so the answer is 6.

In the second example the obtained array b will be [2, -3, 1, -1, 4] so the answer is 7.

In the third example you cannot do anything so the answer is 0.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main {

    static int N, M;
    static int[] A;
    static int[] L, R;

    public static void main(String[] args) {
        FastScanner sc = new FastScanner(System.in);
        N = sc.nextInt();
        M = sc.nextInt();
        A = sc.nextIntArray(N);
        L = new int[M];
        R = new int[M];
        for (int i = 0; i < M; i++) {
            L[i] = sc.nextInt()-1;
            R[i] = sc.nextInt()-1;
        }

        PrintWriter pw = new PrintWriter(System.out);
        solve(pw);
        pw.flush();
    }

    static void solve(PrintWriter pw) {
        Map<Integer, List<int[]>> byL = new HashMap<>();
        Map<Integer, List<int[]>> byR = new HashMap<>();
        for (int i = 0; i < M; i++) {
            int[] lr = {L[i], R[i]};
            if( !byL.containsKey(L[i]) ) {
                byL.put(L[i], new ArrayList<>());
            }
            byL.get(L[i]).add(lr);
            if( !byR.containsKey(R[i]) ) {
                byR.put(R[i], new ArrayList<>());
            }
            byR.get(R[i]).add(lr);
        }

        // とりあえず全部適用する
        int[] imos = new int[N+1];
        for (int i = 0; i < M; i++) {
            imos[L[i]]--;
            imos[R[i]+1]++;
        }
        for (int i = 1; i < N; i++) {
            imos[i] += imos[i-1];
        }
        for (int i = 0; i < N; i++) {
            A[i] += imos[i];
        }
        int min = min(A);
        // debug( A );

        int maxindex = -1;
        int maxDiff = Integer.MIN_VALUE;
        for (int i = 0; i < N; i++) {
            // iがmaxとするとiにかかっているものを解除したくなるのでそうする
            if( byL.containsKey(i) ) {
                List<int[]> lrs = byL.get(i);
                for (int[] lr : lrs) {
                    for (int j = lr[0]; j <= lr[1]; j++) {
                        A[j] += 1;
                    }
                }
                min = min(A);
            }

            // debug(min, A);
            if( A[i] - min > maxDiff ) {
                maxindex = i;
                maxDiff = A[i] - min;
            }

            // iが終わったのでiが終端なものについてまた適用する
            if( byR.containsKey(i) ) {
                List<int[]> lrs = byR.get(i);
                for (int[] lr : lrs) {
                    for (int j = lr[0]; j <= lr[1]; j++) {
                        A[j] -= 1;
                    }
                }
                min = min(A);
            }
        }

        pw.println(maxDiff);
        int cnt = 0;
        List<Integer> applied = new ArrayList<>();
        for (int i = 0; i < M; i++) {
            if( maxindex < L[i] || R[i] < maxindex ) {
                applied.add(i+1);
            }
        }
        pw.println(applied.size());
        StringJoiner j = new StringJoiner(" ");
        for (Integer i : applied) {
            j.add(String.valueOf(i));
        }
        pw.println(j.toString());
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken("\n");
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        int[] nextIntArray(int n, int delta) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt() + delta;
            return a;
        }

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

    static void writeLines(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int a : as) pw.println(a);
        pw.flush();
    }

    static void writeLines(long[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (long a : as) pw.println(a);
        pw.flush();
    }

    static void writeSingleLine(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int i = 0; i < as.length; i++) {
            if (i != 0) pw.print(" ");
            pw.print(as[i]);
        }
        pw.println();
        pw.flush();
    }

    static int max(int... as) {
        int max = Integer.MIN_VALUE;
        for (int a : as) max = Math.max(a, max);
        return max;
    }

    static int min(int... as) {
        int min = Integer.MAX_VALUE;
        for (int a : as) min = Math.min(a, min);
        return min;
    }

    static void debug(Object... args) {
        StringJoiner j = new StringJoiner(" ");
        for (Object arg : args) {
            if (arg == null) j.add("null");
            else if (arg instanceof int[]) j.add(Arrays.toString((int[]) arg));
            else if (arg instanceof long[]) j.add(Arrays.toString((long[]) arg));
            else if (arg instanceof double[]) j.add(Arrays.toString((double[]) arg));
            else if (arg instanceof Object[]) j.add(Arrays.toString((Object[]) arg));
            else j.add(arg.toString());
        }
        System.err.println(j.toString());
    }

    static void printSingleLine(int[] array) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int i = 0; i < array.length; i++) {
            if (i != 0) pw.print(" ");
            pw.print(array[i]);
        }
        pw.println();
        pw.flush();
    }

    static int lowerBound(int[] array, int value) {
        int lo = 0, hi = array.length, mid;
        while (lo < hi) {
            mid = (hi + lo) / 2;
            if (array[mid] < value) lo = mid + 1;
            else hi = mid;
        }
        return lo;
    }

    static int upperBound(int[] array, int value) {
        int lo = 0, hi = array.length, mid;
        while (lo < hi) {
            mid = (hi + lo) / 2;
            if (array[mid] <= value) lo = mid + 1;
            else hi = mid;
        }
        return lo;
    }
}