Problem: You are given an array a_0, a_1, ..., a_{N-1} of length N. Process Q queries of the following types.

* `0 l r b c`: For each i = l, l+1, \dots, {r - 1}, set a_i \gets b \times a_i + c.
* `1 l r`: Print \sum_{i = l}^{r - 1} a_i \bmod 998244353.

Constraints

* 1 \leq N, Q \leq 500000
* 0 \leq a_i, c < 998244353
* 1 \leq b < 998244353
* 0 \leq l < r \leq N
* All values in Input are integer.

Input

Input is given from Standard Input in the following format:


N Q
a_0 a_1 ... a_{N - 1}
\textrm{Query}_0
\textrm{Query}_1
:
\textrm{Query}_{Q - 1}


Output

For each query of the latter type, print the answer.

Example

Input

5 7
1 2 3 4 5
1 0 5
0 2 4 100 101
1 0 3
0 1 3 102 103
1 2 5
0 2 5 104 105
1 0 5


Output

15
404
41511
4317767

Solution (in JAVA):

Solution:
public class Main {
    static final long mod = 998244353;
    public static void main(String[] args) {
        var sc = new FastScanner(System.in);
        var pw = new FastPrintStream();
        final int N = sc.nextInt();
        final int Q = sc.nextInt();
        final var A = new S[N];
        java.util.Arrays.setAll(A, i -> new S(sc.nextLong(), 1));
        var t = new LazySegTree<S, F>(A, S::op, S.E, Main::map, F::composite, F.I);
        for (int i = 0; i < Q; i++) {
            int query = sc.nextInt();
            int l = sc.nextInt();
            int r = sc.nextInt();
            if (query == 0) {
                int a = sc.nextInt();
                int b = sc.nextInt();
                t.apply(l, r, new F(a, b));
            } else {
                pw.println(t.prod(l, r));
            }
        }
        sc.close();
        pw.flush();
        pw.close();
    }
 
    static long add(long u, long v) {
        long s = u + v;
        return s >= mod ? s - mod : s;
    }
 
    static S map(F f, S s) {
        return new S((f.a * s.sum + f.b * s.size) % mod, s.size);
    }
 
    static class S {
        static final S E = new S(0, 0);
        long sum;
        int size;
        public S (long s, int size) {
            this.sum = s;
            this.size = size;
        }
        public static S op(S l, S r) {
            long s = l.sum + r.sum;
            return new S(s >= mod ? s - mod : s, l.size + r.size);
        }
        public String toString() {
            return String.valueOf(sum);
        }
    }
 
    static class F {
        static final F I = new F(1, 0);
        long a, b;
        public F (long a, long b) {
            this.a = a; this.b = b;
        }
        public static F composite(F f, F g) {
            return new F((f.a * g.a) % mod, (f.a * g.b + f.b) % mod);
        }
    }
}

/**
 * TODO: verify {@link LazySegTree#maxRight} and {@link LazySegTree#minLeft}
 * 
 * @verified https://atcoder.jp/contests/practice2/tasks/practice2_k
 */

class LazySegTree<S, F> {
    final int MAX;

    final int N;
    final int Log;
    final java.util.function.BinaryOperator<S> Op;
    final S E;
    final java.util.function.BiFunction<F, S, S> Mapping;
    final java.util.function.BinaryOperator<F> Composition;
    final F Id;

    final S[] Dat;
    final F[] Laz;

    @SuppressWarnings("unchecked")
    public LazySegTree(int n, java.util.function.BinaryOperator<S> op, S e, java.util.function.BiFunction<F, S, S> mapping, java.util.function.BinaryOperator<F> composition, F id) {
        this.MAX = n;
        int k = 1;
        while (k < n) k <<= 1;
        this.N = k;
        this.Log = Integer.numberOfTrailingZeros(N);
        this.Op = op;
        this.E = e;
        this.Mapping = mapping;
        this.Composition = composition;
        this.Id = id;
        this.Dat = (S[]) new Object[N << 1];
        this.Laz = (F[]) new Object[N];
        java.util.Arrays.fill(Dat, E);
        java.util.Arrays.fill(Laz, Id);
    }

    public LazySegTree(S[] dat, java.util.function.BinaryOperator<S> op, S e, java.util.function.BiFunction<F, S, S> mapping, java.util.function.BinaryOperator<F> composition, F id) {
        this(dat.length, op, e, mapping, composition, id);
        build(dat);
    }

    private void build(S[] dat) {
        int l = dat.length;
        System.arraycopy(dat, 0, Dat, N, l);
        for (int i = N - 1; i > 0; i--) {
            Dat[i] = Op.apply(Dat[i << 1 | 0], Dat[i << 1 | 1]);
        }
    }

    private void push(int k) {
        if (Laz[k] == Id) return;
        int lk = k << 1 | 0, rk = k << 1 | 1;
        Dat[lk] = Mapping.apply(Laz[k], Dat[lk]);
        Dat[rk] = Mapping.apply(Laz[k], Dat[rk]);
        if (lk < N) Laz[lk] = Composition.apply(Laz[k], Laz[lk]);
        if (rk < N) Laz[rk] = Composition.apply(Laz[k], Laz[rk]);
        Laz[k] = Id;
    }

    private void pushTo(int k) {
        for (int i = Log; i > 0; i--) push(k >> i);
    }

    private void pushTo(int lk, int rk) {
        for (int i = Log; i > 0; i--) {
            if (((lk >> i) << i) != lk) push(lk >> i);
            if (((rk >> i) << i) != rk) push(rk >> i);
        }
    }

    private void updateFrom(int k) {
        k >>= 1;
        while (k > 0) {
            Dat[k] = Op.apply(Dat[k << 1 | 0], Dat[k << 1 | 1]);
            k >>= 1;
        }
    }

    private void updateFrom(int lk, int rk) {
        for (int i = 1; i <= Log; i++) {
            if (((lk >> i) << i) != lk) {
                int lki = lk >> i;
                Dat[lki] = Op.apply(Dat[lki << 1 | 0], Dat[lki << 1 | 1]);
            }
            if (((rk >> i) << i) != rk) {
                int rki = (rk - 1) >> i;
                Dat[rki] = Op.apply(Dat[rki << 1 | 0], Dat[rki << 1 | 1]);
            }
        }
    }

    public void set(int p, S x) {
        exclusiveRangeCheck(p);
        p += N;
        pushTo(p);
        Dat[p] = x;
        updateFrom(p);
    }

    public S get(int p) {
        exclusiveRangeCheck(p);
        p += N;
        pushTo(p);
        return Dat[p];
    }

    public S prod(int l, int r) {
        if (l > r) {
            throw new IllegalArgumentException(
                String.format("Invalid range: [%d, %d)", l, r)
            );
        }
        inclusiveRangeCheck(l);
        inclusiveRangeCheck(r);
        if (l == r) return E;
        l += N; r += N;
        pushTo(l, r);
        S sumLeft = E, sumRight = E;
        while (l < r) {
            if ((l & 1) == 1) sumLeft = Op.apply(sumLeft, Dat[l++]);
            if ((r & 1) == 1) sumRight = Op.apply(Dat[--r], sumRight);
            l >>= 1; r >>= 1;
        }
        return Op.apply(sumLeft, sumRight);
    }

    public S allProd() {
        return Dat[1];
    }

    public void apply(int p, F f) {
        exclusiveRangeCheck(p);
        p += N;
        pushTo(p);
        Dat[p] = Mapping.apply(f, Dat[p]);
        updateFrom(p);
    }

    public void apply(int l, int r, F f) {
        if (l > r) {
            throw new IllegalArgumentException(
                String.format("Invalid range: [%d, %d)", l, r)
            );
        }
        inclusiveRangeCheck(l);
        inclusiveRangeCheck(r);
        if (l == r) return;
        l += N; r += N;
        pushTo(l, r);
        for (int l2 = l, r2 = r; l2 < r2;) {
            if ((l2 & 1) == 1) {
                Dat[l2] = Mapping.apply(f, Dat[l2]);
                if (l2 < N) Laz[l2] = Composition.apply(f, Laz[l2]);
                l2++;
            }
            if ((r2 & 1) == 1) {
                r2--;
                Dat[r2] = Mapping.apply(f, Dat[r2]);
                if (r2 < N) Laz[r2] = Composition.apply(f, Laz[r2]);
            }
            l2 >>= 1; r2 >>= 1;
        }
        updateFrom(l, r);
    }

    public int maxRight(int l, java.util.function.Predicate<S> g) {
        inclusiveRangeCheck(l);
        if (!g.test(E)) {
            throw new IllegalArgumentException("Identity element must satisfy the condition.");
        }
        if (l == MAX) return MAX;
        l += N;
        pushTo(l);
        S sum = E;
        do {
            l >>= Integer.numberOfTrailingZeros(l);
            if (!g.test(Op.apply(sum, Dat[l]))) {
                while (l < N) {
                    push(l);
                    l = l << 1;
                    if (g.test(Op.apply(sum, Dat[l]))) {
                        sum = Op.apply(sum, Dat[l]);
                        l++;
                    }
                }
                return l - N;
            }
            sum = Op.apply(sum, Dat[l]);
            l++;
        } while ((l & -l) != l);
        return MAX;
    }

    public int minLeft(int r, java.util.function.Predicate<S> g) {
        inclusiveRangeCheck(r);
        if (!g.test(E)) {
            throw new IllegalArgumentException("Identity element must satisfy the condition.");
        }
        if (r == 0) return 0;
        r += N;
        pushTo(r - 1);
        S sum = E;
        do {
            r--;
            while (r > 1 && (r & 1) == 1) r >>= 1;
            if (!g.test(Op.apply(Dat[r], sum))) {
                while (r < N) {
                    push(r);
                    r = r << 1 | 1;
                    if (g.test(Op.apply(Dat[r], sum))) {
                        sum = Op.apply(Dat[r], sum);
                        r--;
                    }
                }
                return r + 1 - N;
            }
            sum = Op.apply(Dat[r], sum);
        } while ((r & -r) != r);
        return 0;
    }

    private void exclusiveRangeCheck(int p) {
        if (p < 0 || p >= MAX) {
            throw new IndexOutOfBoundsException(
                String.format("Index %d is not in [%d, %d).", p, 0, MAX)
            );
        }
    }

    private void inclusiveRangeCheck(int p) {
        if (p < 0 || p > MAX) {
            throw new IndexOutOfBoundsException(
                String.format("Index %d is not in [%d, %d].", p, 0, MAX)
            );
        }
    }
}

class FastPrintStream implements AutoCloseable {
    private static final int BUF_SIZE = 1 << 15;
    private final byte[] buf = new byte[BUF_SIZE];
    private int ptr = 0;
    private final java.lang.reflect.Field strField;
    private final java.nio.charset.CharsetEncoder encoder;

    private java.io.OutputStream out;

    public FastPrintStream(java.io.OutputStream out) {
        this.out = out;
        java.lang.reflect.Field f;
        try {
            f = java.lang.String.class.getDeclaredField("value");
            f.setAccessible(true);
        } catch (NoSuchFieldException | SecurityException e) {
            f = null;
        }
        this.strField = f;
        this.encoder = java.nio.charset.StandardCharsets.US_ASCII.newEncoder();
    }

    public FastPrintStream(java.io.File file) throws java.io.IOException {
        this(new java.io.FileOutputStream(file));
    }

    public FastPrintStream(java.lang.String filename) throws java.io.IOException {
        this(new java.io.File(filename));
    }

    public FastPrintStream() {
        this(System.out);
        try {
            java.lang.reflect.Field f = java.io.PrintStream.class.getDeclaredField("autoFlush");
            f.setAccessible(true);
            f.set(System.out, false);
        } catch (IllegalAccessException | IllegalArgumentException | NoSuchFieldException e) {
            // ignore
        }
    }

    public FastPrintStream println() {
        if (ptr == BUF_SIZE) internalFlush();
        buf[ptr++] = (byte) '\n';
        return this;
    }

    public FastPrintStream println(java.lang.Object o) {
        return print(o).println();
    }

    public FastPrintStream println(java.lang.String s) {
        return print(s).println();
    }

    public FastPrintStream println(char[] s) {
        return print(s).println();
    }

    public FastPrintStream println(char c) {
        return print(c).println();
    }

    public FastPrintStream println(int x) {
        return print(x).println();
    }

    public FastPrintStream println(long x) {
        return print(x).println();
    }

    public FastPrintStream println(double d, int precision) {
        return print(d, precision).println();
    }

    private FastPrintStream print(byte[] bytes) {
        int n = bytes.length;
        if (ptr + n > BUF_SIZE) {
            internalFlush();
            try {
                out.write(bytes);
            } catch (java.io.IOException e) {
                throw new RuntimeException();
            }
        } else {
            System.arraycopy(bytes, 0, buf, ptr, n);
            ptr += n;
        }
        return this;
    }

    public FastPrintStream print(java.lang.Object o) {
        return print(o.toString());
    }

    public FastPrintStream print(java.lang.String s) {
        if (strField == null) {
            return print(s.getBytes());
        } else {
            try {
                return print((byte[]) strField.get(s));
            } catch (IllegalAccessException e) {
                return print(s.getBytes());
            }
        }
    }

    public FastPrintStream print(char[] s) {
        try {
            return print(encoder.encode(java.nio.CharBuffer.wrap(s)).array());
        } catch (java.nio.charset.CharacterCodingException e) {
            byte[] bytes = new byte[s.length];
            for (int i = 0; i < s.length; i++) {
                bytes[i] = (byte) s[i];
            }
            return print(bytes);
        }
    }

    public FastPrintStream print(char c) {
        if (ptr == BUF_SIZE) internalFlush();
        buf[ptr++] = (byte) c;
        return this;
    }

    public FastPrintStream print(int x) {
        if (x == 0) {
            if (ptr == BUF_SIZE) internalFlush();
            buf[ptr++] = '0';
            return this;
        }
        int d = len(x);
        if (ptr + d > BUF_SIZE) internalFlush();
        if (x < 0) {
            buf[ptr++] = '-';
            x = -x;
            d--;
        }
        int j = ptr += d; 
        while (x > 0) {
            buf[--j] = (byte) ('0' + (x % 10));
            x /= 10;
        }
        return this;
    }

    public FastPrintStream print(long x) {
        if (x == 0) {
            if (ptr == BUF_SIZE) internalFlush();
            buf[ptr++] = '0';
            return this;
        }
        int d = len(x);
        if (ptr + d > BUF_SIZE) internalFlush();
        if (x < 0) {
            buf[ptr++] = '-';
            x = -x;
            d--;
        }
        int j = ptr += d; 
        while (x > 0) {
            buf[--j] = (byte) ('0' + (x % 10));
            x /= 10;
        }
        return this;
    }

    public FastPrintStream print(double d, int precision) {
        if (d < 0) {
            print('-');
            d = -d;
        }
        d += Math.pow(10, -d) / 2;
        print((long) d).print('.');
        d -= (long) d;
        for(int i = 0; i < precision; i++){
            d *= 10;
            print((int) d);
            d -= (int) d;
        }
        return this;
    }

    private void internalFlush() {
        try {
            out.write(buf, 0, ptr);
            ptr = 0;
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
    }

    public void flush() {
        try {
            out.write(buf, 0, ptr);
            out.flush();
            ptr = 0;
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
    }

    public void close() {
        try {
            out.close();
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
    }

    private static int len(int x) {
        int d = 1;
        if (x >= 0) {d = 0; x = -x;}
        int p = -10;
        for (int i = 1; i < 10; i++, p *= 10) if (x > p) return i + d;
        return 10 + d;
    }

    private static int len(long x) {
        int d = 1;
        if (x >= 0) {d = 0; x = -x;}
        long p = -10;
        for (int i = 1; i < 19; i++, p *= 10) if (x > p) return i + d;
        return 19 + d;
    }
}

class FastScanner implements AutoCloseable {
    private final java.io.InputStream in;
    private final byte[] buf = new byte[2048];
    private int ptr = 0;
    private int buflen = 0;

    public FastScanner(java.io.InputStream in) {
        this.in = in;
    }

    public FastScanner() {
        this(System.in);
    }

    private boolean hasNextByte() {
        if (ptr < buflen) return true;
        ptr = 0;
        try {
            buflen = in.read(buf);
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
        return buflen > 0;
    }

    private int readByte() {
        return hasNextByte() ? buf[ptr++] : -1;
    }

    public boolean hasNext() {
        while (hasNextByte() && !(32 < buf[ptr] && buf[ptr] < 127)) ptr++;
        return hasNextByte();
    }

    private StringBuilder nextSequence() {
        if (!hasNext()) throw new java.util.NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        for (int b = readByte(); 32 < b && b < 127; b = readByte()) {
            sb.appendCodePoint(b);
        }
        return sb;
    }

    public String next() {
        return nextSequence().toString();
    }

    public String next(int len) {
        return new String(nextChars(len));
    }

    public char nextChar() {
        if (!hasNextByte()) throw new java.util.NoSuchElementException();
        return (char) readByte();
    }

    public char[] nextChars() {
        StringBuilder sb = nextSequence();
        int l = sb.length();
        char[] dst = new char[l];
        sb.getChars(0, l, dst, 0);
        return dst;
    }
    public char[] nextChars(int len) {
        if (!hasNext()) throw new java.util.NoSuchElementException();
        char[] s = new char[len];
        int i = 0;
        int b = readByte();
        while (32 < b && b < 127 && i < len) {
            s[i++] = (char) b; b = readByte();
        }
        if (i != len) {
            throw new java.util.NoSuchElementException(
                String.format("Next token has smaller length than expected.", len)
            );
        }
        return s;
    }
    public long nextLong() {
        if (!hasNext()) throw new java.util.NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) throw new NumberFormatException();
        while (true) {
            if ('0' <= b && b <= '9') {
                n = n * 10 + b - '0';
            } else if (b == -1 || !(32 < b && b < 127)) {
                return minus ? -n : n;
            } else throw new NumberFormatException();
            b = readByte();
        }
    }
    public int nextInt() {
        return Math.toIntExact(nextLong());
    }
    public double nextDouble() {
        return Double.parseDouble(next());
    }
    public void close() {
        try {
            in.close();
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
    }
}