Problem:
 Score : 100 points    Problem Statement You are given two integer arrays a_0, a_1, ..., a_{N - 1} and b_0, b_1, ..., b_{M - 1} . Calculate the array c_0, c_1, ..., c_{(N - 1) + (M - 1)} , defined by c_i = \sum_{j = 0}^i a_j b_{i - j} \bmod 998244353 .      Constraints  1 \leq N, M \leq 524288  0 \leq a_i, b_i < 998244353  All values in Input are integer.         Input Input is given from Standard Input in the following format:  N  M  a_0  a_1 ... a_{N-1}  b_0  b_1 ... b_{M-1}       Output Print the answer in the following format:  c_0  c_1 ... c_{(N - 1) + (M - 1)}         Sample Input 1 4 5
1 2 3 4
5 6 7 8 9      Sample Output 1 5 16 34 60 70 70 59 36       Sample Input 2 1 1
10000000
10000000      Sample Output 2 871938225

Solution (Python):
import numpy as np

MOD = 998244353

N, M = map(int, input().split())
As = list(map(int, input().split()))
Bs = list(map(int, input().split()))

def divideArr3(As, numD):
    arrA = np.array(As, dtype=np.int64)
    mask = (1<<numD) - 1
    arrA0 = arrA & mask
    arrA1 = (arrA>>numD) & mask
    arrA2 = arrA>>(2*numD)
    return arrA2, arrA1, arrA0

def convolveArr(arrA, arrB):
    L = len(arrA) + len(arrB) - 1
    lenFFT = 1 << ((L-1).bit_length())
    fA = np.fft.rfft(arrA, n=lenFFT)
    fB = np.fft.rfft(arrB, n=lenFFT)
    arrC = np.rint(np.fft.irfft(fA * fB, n=lenFFT)).astype(np.int64)
    return arrC[:L]

def convolveMOD(As, Bs, MOD):
    numD = 10
    div = 1<<numD
    arrA2, arrA1, arrA0 = divideArr3(As, numD)
    arrB2, arrB1, arrB0 = divideArr3(Bs, numD)

    arrC4 = convolveArr(arrA2, arrB2) % MOD
    arrC2 = convolveArr(arrA1, arrB1) % MOD
    arrC0 = convolveArr(arrA0, arrB0) % MOD
    arrC3 = (convolveArr(arrA2+arrA1, arrB2+arrB1) % MOD - arrC4 - arrC2) % MOD
    arrC1 = (convolveArr(arrA1+arrA0, arrB1+arrB0) % MOD - arrC2 - arrC0) % MOD
    arrC2 += (convolveArr(arrA2+arrA0, arrB2+arrB0) % MOD - arrC4 - arrC0) % MOD
    arrC2 %= MOD

    div2 = div*div%MOD
    div3 = div2*div%MOD
    div4 = div3*div%MOD
    arrAns = ((arrC4*div4)%MOD + (arrC3*div3)%MOD + (arrC2*div2)%MOD + (arrC1*div)%MOD + arrC0) % MOD
    return arrAns.tolist()

anss = convolveMOD(As, Bs, MOD)
print(' '.join(map(str, anss)))

Solution (Python):
import numpy as np
from scipy import signal

MOD = 998244353

N, M = map(int, input().split())
As = list(map(int, input().split()))
Bs = list(map(int, input().split()))

def divideArr3(As, numD):
    arrA = np.array(As, dtype=np.int64)
    mask = (1<<numD) - 1
    arrA0 = arrA & mask
    arrA1 = (arrA>>numD) & mask
    arrA2 = arrA>>(2*numD)
    return arrA2, arrA1, arrA0

def convolveArr(arrA, arrB):
    arrC = np.rint(signal.fftconvolve(arrA, arrB)).astype(np.int64)
    return arrC

def convolveMOD(As, Bs, MOD):
    numD = 10
    div = 1<<numD
    arrA2, arrA1, arrA0 = divideArr3(As, numD)
    arrB2, arrB1, arrB0 = divideArr3(Bs, numD)

    arrC4 = convolveArr(arrA2, arrB2) % MOD
    arrC2 = convolveArr(arrA1, arrB1) % MOD
    arrC0 = convolveArr(arrA0, arrB0) % MOD
    arrC3 = (convolveArr(arrA2+arrA1, arrB2+arrB1) % MOD - arrC4 - arrC2) % MOD
    arrC1 = (convolveArr(arrA1+arrA0, arrB1+arrB0) % MOD - arrC2 - arrC0) % MOD
    arrC2 += (convolveArr(arrA2+arrA0, arrB2+arrB0) % MOD - arrC4 - arrC0) % MOD
    arrC2 %= MOD

    div2 = div*div%MOD
    div3 = div2*div%MOD
    div4 = div3*div%MOD
    arrAns = ((arrC4*div4)%MOD + (arrC3*div3)%MOD + (arrC2*div2)%MOD + (arrC1*div)%MOD + arrC0) % MOD
    return arrAns.tolist()

anss = convolveMOD(As, Bs, MOD)
print(' '.join(map(str, anss)))

Solution (Python):
MOD = 998244353


def convolution(a, b):
    def butterfly(arr):
        n = len(arr)
        h = (n - 1).bit_length()
        sum_e = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601,
                 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 0, 0, 0, 0, 0, 0, 0, 0, 0)
        for ph in range(1, h + 1):
            w = 1 << (ph - 1)
            p = 1 << (h - ph)
            now = 1
            for s in range(w):
                offset = s << (h - ph + 1)
                for i in range(p):
                    l = arr[i + offset]
                    r = arr[i + offset + p] * now
                    arr[i + offset] = (l + r) % MOD
                    arr[i + offset + p] = (l - r) % MOD
                now *= sum_e[(~s & -~s).bit_length() - 1]
                now %= MOD

    def butterfly_inv(arr):
        n = len(arr)
        h = (n - 1).bit_length()
        sum_ie = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543,
                  109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 0, 0, 0, 0, 0, 0, 0, 0, 0)
        for ph in range(1, h + 1)[::-1]:
            w = 1 << (ph - 1)
            p = 1 << (h - ph)
            inow = 1
            for s in range(w):
                offset = s << (h - ph + 1)
                for i in range(p):
                    l = arr[i + offset]
                    r = arr[i + offset + p]
                    arr[i + offset] = (l + r) % MOD
                    arr[i + offset + p] = (MOD + l - r) * inow % MOD
                inow *= sum_ie[(~s & -~s).bit_length() - 1]
                inow %= MOD

    n = len(a)
    m = len(b)
    if not n or not m:
        return []
    if min(n, m) <= 50:
        if n < m:
            n, m = m, n
            a, b = b, a
        res = [0] * (n + m - 1)
        for i in range(n):
            for j in range(m):
                res[i + j] += a[i] * b[j]
                res[i + j] %= MOD
        return res
    z = 1 << (n + m - 2).bit_length()
    a += [0] * (z - n)
    b += [0] * (z - m)
    butterfly(a)
    butterfly(b)
    for i in range(z):
        a[i] *= b[i]
        a[i] %= MOD
    butterfly_inv(a)
    a = a[:n + m - 1]
    iz = pow(z, MOD - 2, MOD)
    for i in range(n + m - 1):
        a[i] *= iz
        a[i] %= MOD
    return a


def atcoder_practice2_f():
    import sys
    input = sys.stdin.buffer.readline

    N, M = map(int, input().split())
    A = [int(x) for x in input().split()]
    B = [int(x) for x in input().split()]

    print(*convolution(A, B))


if __name__ == "__main__":
    atcoder_practice2_f()

Solution (Python):
MOD = 998244353

def convolution(a, b):
    def butterfly(arr):
        n = len(arr)
        h = (n - 1).bit_length()
        sum_e = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601,
                842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 0, 0, 0, 0, 0, 0, 0, 0, 0)
        for ph in range(1, h + 1):
            w = 1 << (ph - 1)
            p = 1 << (h - ph)
            now = 1
            for s in range(w):
                offset = s << (h - ph + 1)
                for i in range(p):
                    l = arr[i + offset]
                    r = arr[i + offset + p] * now
                    arr[i + offset] = (l + r) % MOD
                    arr[i + offset + p] = (l - r) % MOD
                now *= sum_e[(~s & -~s).bit_length() - 1]
                now %= MOD


    def butterfly_inv(arr):
        n = len(arr)
        h = (n - 1).bit_length()
        sum_ie = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543,
                109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 0, 0, 0, 0, 0, 0, 0, 0, 0)
        for ph in range(1, h + 1)[::-1]:
            w = 1 << (ph - 1)
            p = 1 << (h - ph)
            inow = 1
            for s in range(w):
                offset = s << (h - ph + 1)
                for i in range(p):
                    l = arr[i + offset]
                    r = arr[i + offset + p]
                    arr[i + offset] = (l + r) % MOD
                    arr[i + offset + p] = (MOD + l - r) * inow % MOD
                inow *= sum_ie[(~s & -~s).bit_length() - 1]
                inow %= MOD

    n = len(a)
    m = len(b)
    if not n or not m: return []
    if min(n, m) <= 50:
        if n < m:
            n, m = m, n
            a, b = b, a
        res = [0] * (n + m - 1)
        for i in range(n):
            for j in range(m):
                res[i + j] += a[i] * b[j]
                res[i + j] %= MOD
        return res
    z = 1 << (n + m - 2).bit_length()
    a += [0] * (z - n)
    b += [0] * (z - m)
    butterfly(a)
    butterfly(b)
    for i in range(z):
        a[i] *= b[i]
        a[i] %= MOD
    butterfly_inv(a)
    a = a[:n + m - 1]
    iz = pow(z, MOD - 2, MOD)
    for i in range(n + m - 1):
        a[i] *= iz
        a[i] %= MOD
    return a


def atcoder_practice2_f():
    import sys
    input = sys.stdin.buffer.readline

    N, M = map(int, input().split())
    A = [int(x) for x in input().split()]
    B = [int(x) for x in input().split()]

    print(*convolution(A, B))


if __name__ == "__main__":
    atcoder_practice2_f()

Solution (Python):

MOD = 998244353
sum_e = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 0, 0, 0, 0, 0, 0, 0, 0, 0)
sum_ie = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 0, 0, 0, 0, 0, 0, 0, 0, 0)
class Convolution:
    
    def __init__(self):
        pass
        
        
        

    def __butterfly(self, arr):
        n = len(arr)
        h = (n - 1).bit_length()
        

        for ph in range(1, h + 1):
            w = 1 << (ph - 1)
            p = 1 << (h - ph)
            now = 1
            for s in range(w):
                offset = s << (h - ph + 1)
                for i in range(p):
                    l = arr[i + offset]
                    r = arr[i + offset + p] * now
                    arr[i + offset] = (l + r) % MOD
                    arr[i + offset + p] = (l - r) % MOD
                now *= sum_e[(~s & -~s).bit_length() - 1]
                now %= MOD

    def __butterfly_inv(self, arr):
        n = len(arr)
        h = (n - 1).bit_length()
        

        for ph in range(1, h + 1)[::-1]:
            w = 1 << (ph - 1)
            p = 1 << (h - ph)
            inow = 1
            for s in range(w):
                offset = s << (h - ph + 1)
                for i in range(p):
                    l = arr[i + offset]
                    r = arr[i + offset + p]
                    arr[i + offset] = (l + r) % MOD
                    arr[i + offset + p] = (MOD + l - r) * inow % MOD
                inow *= sum_ie[(~s & -~s).bit_length() - 1]
                inow %= MOD

    def __call__(self, a, b):
        n = len(a)
        m = len(b)
        
        if not n or not m: return []
        if min(n, m) <= 50:
            if n < m:
                n, m = m, n
                a, b = b, a
            res = [0] * (n + m - 1)
            for i in range(n):
                for j in range(m):
                    res[i + j] += a[i] * b[j]
                    res[i + j] %= MOD
            return res
        z = 1 << (n + m - 2).bit_length()
        a += [0] * (z - n)
        b += [0] * (z - m)
        self.__butterfly(a)
        self.__butterfly(b)
        for i in range(z):
            a[i] *= b[i]
            a[i] %= MOD
        self.__butterfly_inv(a)
        a = a[:n + m - 1]
        iz = pow(z, MOD - 2, MOD)
        for i in range(n + m - 1):
            a[i] *= iz
            a[i] %= MOD
        return a




def atcoder_practice2_f():
    import sys
    input = sys.stdin.buffer.readline

    N, M = map(int, input().split())
    A = [int(x) for x in input().split()]
    B = [int(x) for x in input().split()]

    convolution = Convolution()
    print(*convolution(A, B))


if __name__ == "__main__":
    atcoder_practice2_f()

Solution (Python):
MOD = 998244353

def butterfly(arr):
    n = len(arr)
    h = (n - 1).bit_length()
    sum_e = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601,
                842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 0, 0, 0, 0, 0, 0, 0, 0, 0)
    for ph in range(1, h + 1):
        w = 1 << (ph - 1)
        p = 1 << (h - ph)
        now = 1
        for s in range(w):
            offset = s << (h - ph + 1)
            for i in range(p):
                l = arr[i + offset]
                r = arr[i + offset + p] * now
                arr[i + offset] = (l + r) % MOD
                arr[i + offset + p] = (l - r) % MOD
            now *= sum_e[(~s & -~s).bit_length() - 1]
            now %= MOD

def butterfly_inv(arr):
    n = len(arr)
    h = (n - 1).bit_length()
    sum_ie = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543,
                109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 0, 0, 0, 0, 0, 0, 0, 0, 0)
    for ph in range(1, h + 1)[::-1]:
        w = 1 << (ph - 1)
        p = 1 << (h - ph)
        inow = 1
        for s in range(w):
            offset = s << (h - ph + 1)
            for i in range(p):
                l = arr[i + offset]
                r = arr[i + offset + p]
                arr[i + offset] = (l + r) % MOD
                arr[i + offset + p] = (MOD + l - r) * inow % MOD
            inow *= sum_ie[(~s & -~s).bit_length() - 1]
            inow %= MOD



def convolution(a, b):
    n = len(a)
    m = len(b)
    if not n or not m: return []
    if min(n, m) <= 50:
        if n < m:
            n, m = m, n
            a, b = b, a
        res = [0] * (n + m - 1)
        for i in range(n):
            for j in range(m):
                res[i + j] += a[i] * b[j]
                res[i + j] %= MOD
        return res
    z = 1 << (n + m - 2).bit_length()
    a += [0] * (z - n)
    b += [0] * (z - m)
    butterfly(a)
    butterfly(b)
    for i in range(z):
        a[i] *= b[i]
        a[i] %= MOD
    butterfly_inv(a)
    a = a[:n + m - 1]
    iz = pow(z, MOD - 2, MOD)
    for i in range(n + m - 1):
        a[i] *= iz
        a[i] %= MOD
    return a


def atcoder_practice2_f():
    import sys
    input = sys.stdin.buffer.readline

    N, M = map(int, input().split())
    A = [int(x) for x in input().split()]
    B = [int(x) for x in input().split()]

    print(*convolution(A, B))


if __name__ == "__main__":
    atcoder_practice2_f()

Solution (Python):

def butterfly(arr, MOD):
    n = len(arr)
    h = (n - 1).bit_length()
    sum_e = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601,
                842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 0, 0, 0, 0, 0, 0, 0, 0, 0)
    for ph in range(1, h + 1):
        w = 1 << (ph - 1)
        p = 1 << (h - ph)
        now = 1
        for s in range(w):
            offset = s << (h - ph + 1)
            for i in range(p):
                l = arr[i + offset]
                r = arr[i + offset + p] * now
                arr[i + offset] = (l + r) % MOD
                arr[i + offset + p] = (l - r) % MOD
            now *= sum_e[(~s & -~s).bit_length() - 1]
            now %= MOD

def butterfly_inv(arr, MOD):
    n = len(arr)
    h = (n - 1).bit_length()
    sum_ie = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543,
                109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 0, 0, 0, 0, 0, 0, 0, 0, 0)
    for ph in range(1, h + 1)[::-1]:
        w = 1 << (ph - 1)
        p = 1 << (h - ph)
        inow = 1
        for s in range(w):
            offset = s << (h - ph + 1)
            for i in range(p):
                l = arr[i + offset]
                r = arr[i + offset + p]
                arr[i + offset] = (l + r) % MOD
                arr[i + offset + p] = (MOD + l - r) * inow % MOD
            inow *= sum_ie[(~s & -~s).bit_length() - 1]
            inow %= MOD



def convolution(a, b, MOD=10**9+7):
    n = len(a)
    m = len(b)
    if not n or not m: return []
    if min(n, m) <= 50:
        if n < m:
            n, m = m, n
            a, b = b, a
        res = [0] * (n + m - 1)
        for i in range(n):
            for j in range(m):
                res[i + j] += a[i] * b[j]
                res[i + j] %= MOD
        return res
    z = 1 << (n + m - 2).bit_length()
    a += [0] * (z - n)
    b += [0] * (z - m)
    butterfly(a, MOD)
    butterfly(b, MOD)
    for i in range(z):
        a[i] *= b[i]
        a[i] %= MOD
    butterfly_inv(a, MOD)
    a = a[:n + m - 1]
    iz = pow(z, MOD - 2, MOD)
    for i in range(n + m - 1):
        a[i] *= iz
        a[i] %= MOD
    return a

import sys
input = sys.stdin.buffer.readline

N, M = map(int, input().split())
A = [int(x) for x in input().split()]
B = [int(x) for x in input().split()]

print(*convolution(A, B, 998244353))

Solution (Python):
def convolution(a, b, MOD=10**9+7):
    def butterfly(arr):
        n = len(arr)
        h = (n - 1).bit_length()
        sum_e = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601,
                 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 0, 0, 0, 0, 0, 0, 0, 0, 0)
        for ph in range(1, h + 1):
            w = 1 << (ph - 1)
            p = 1 << (h - ph)
            now = 1
            for s in range(w):
                offset = s << (h - ph + 1)
                for i in range(p):
                    l = arr[i + offset]
                    r = arr[i + offset + p] * now
                    arr[i + offset] = (l + r) % MOD
                    arr[i + offset + p] = (l - r) % MOD
                now *= sum_e[(~s & -~s).bit_length() - 1]
                now %= MOD


    def butterfly_inv(arr):
        n = len(arr)
        h = (n - 1).bit_length()
        sum_ie = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543,
                  109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 0, 0, 0, 0, 0, 0, 0, 0, 0)
        for ph in range(1, h + 1)[::-1]:
            w = 1 << (ph - 1)
            p = 1 << (h - ph)
            inow = 1
            for s in range(w):
                offset = s << (h - ph + 1)
                for i in range(p):
                    l = arr[i + offset]
                    r = arr[i + offset + p]
                    arr[i + offset] = (l + r) % MOD
                    arr[i + offset + p] = (MOD + l - r) * inow % MOD
                inow *= sum_ie[(~s & -~s).bit_length() - 1]
                inow %= MOD


    n = len(a)
    m = len(b)
    if not n or not m: return []
    if min(n, m) <= 50:
        if n < m:
            n, m = m, n
            a, b = b, a
        res = [0] * (n + m - 1)
        for i in range(n):
            for j in range(m):
                res[i + j] += a[i] * b[j]
                res[i + j] %= MOD
        return res
    z = 1 << (n + m - 2).bit_length()
    a += [0] * (z - n)
    b += [0] * (z - m)
    butterfly(a)
    butterfly(b)
    for i in range(z):
        a[i] *= b[i]
        a[i] %= MOD
    butterfly_inv(a)
    a = a[:n + m - 1]
    iz = pow(z, MOD - 2, MOD)
    for i in range(n + m - 1):
        a[i] *= iz
        a[i] %= MOD
    return a

import sys
input = sys.stdin.buffer.readline

N, M = map(int, input().split())
A = [int(x) for x in input().split()]
B = [int(x) for x in input().split()]

print(*convolution(A, B, 998244353))

Solution (Python):
def convolution(a, b, MOD=10**9+7):
    def butterfly(arr):
        n = len(arr)
        h = (n - 1).bit_length()
        sum_e = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601,
                 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 0, 0, 0, 0, 0, 0, 0, 0, 0)
        for ph in range(1, h + 1):
            w = 1 << (ph - 1)
            p = 1 << (h - ph)
            now = 1
            for s in range(w):
                offset = s << (h - ph + 1)
                for i in range(p):
                    l = arr[i + offset]
                    r = arr[i + offset + p] * now
                    arr[i + offset] = (l + r) % MOD
                    arr[i + offset + p] = (l - r) % MOD
                now *= sum_e[(~s & -~s).bit_length() - 1]
                now %= MOD


    def butterfly_inv(arr):
        n = len(arr)
        h = (n - 1).bit_length()
        sum_ie = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543,
                  109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 0, 0, 0, 0, 0, 0, 0, 0, 0)
        for ph in range(1, h + 1)[::-1]:
            w = 1 << (ph - 1)
            p = 1 << (h - ph)
            inow = 1
            for s in range(w):
                offset = s << (h - ph + 1)
                for i in range(p):
                    l = arr[i + offset]
                    r = arr[i + offset + p]
                    arr[i + offset] = (l + r) % MOD
                    arr[i + offset + p] = (MOD + l - r) * inow % MOD
                inow *= sum_ie[(~s & -~s).bit_length() - 1]
                inow %= MOD


    n = len(a)
    m = len(b)
    if not n or not m: return []
    if min(n, m) <= 50:
        if n < m:
            n, m = m, n
            a, b = b, a
        res = [0] * (n + m - 1)
        for i in range(n):
            for j in range(m):
                res[i + j] += a[i] * b[j]
                res[i + j] %= MOD
        return res
    z = 1 << (n + m - 2).bit_length()
    a += [0] * (z - n)
    b += [0] * (z - m)
    butterfly(a)
    butterfly(b)
    for i in range(z):
        a[i] *= b[i]
        a[i] %= MOD
    butterfly_inv(a)
    a = a[:n + m - 1]
    iz = pow(z, MOD - 2, MOD)
    for i in range(n + m - 1):
        a[i] *= iz
        a[i] %= MOD
    return a


def atcoder_practice2_f():
    import sys
    input = sys.stdin.buffer.readline

    N, M = map(int, input().split())
    A = [int(x) for x in input().split()]
    B = [int(x) for x in input().split()]

    print(*convolution(A, B, 998244353))


if __name__ == "__main__":
    atcoder_practice2_f()

Solution (Python):

MOD = None
sum_e = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 0, 0, 0, 0, 0, 0, 0, 0, 0)
sum_ie = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 0, 0, 0, 0, 0, 0, 0, 0, 0)
class Convolution:

    
    def __init__(self, mod):
        global MOD
        MOD = mod
        

    def __butterfly(self, arr):
        n = len(arr)
        h = (n - 1).bit_length()
        

        for ph in range(1, h + 1):
            w = 1 << (ph - 1)
            p = 1 << (h - ph)
            now = 1
            for s in range(w):
                offset = s << (h - ph + 1)
                for i in range(p):
                    l = arr[i + offset]
                    r = arr[i + offset + p] * now
                    arr[i + offset] = (l + r) % MOD
                    arr[i + offset + p] = (l - r) % MOD
                now *= sum_e[(~s & -~s).bit_length() - 1]
                now %= MOD

    def __butterfly_inv(self, arr):
        n = len(arr)
        h = (n - 1).bit_length()
        

        for ph in range(1, h + 1)[::-1]:
            w = 1 << (ph - 1)
            p = 1 << (h - ph)
            inow = 1
            for s in range(w):
                offset = s << (h - ph + 1)
                for i in range(p):
                    l = arr[i + offset]
                    r = arr[i + offset + p]
                    arr[i + offset] = (l + r) % MOD
                    arr[i + offset + p] = (MOD + l - r) * inow % MOD
                inow *= sum_ie[(~s & -~s).bit_length() - 1]
                inow %= MOD

    def __call__(self, a, b):
        n = len(a)
        m = len(b)
        
        if not n or not m: return []
        if min(n, m) <= 50:
            if n < m:
                n, m = m, n
                a, b = b, a
            res = [0] * (n + m - 1)
            for i in range(n):
                for j in range(m):
                    res[i + j] += a[i] * b[j]
                    res[i + j] %= MOD
            return res
        z = 1 << (n + m - 2).bit_length()
        a += [0] * (z - n)
        b += [0] * (z - m)
        self.__butterfly(a)
        self.__butterfly(b)
        for i in range(z):
            a[i] *= b[i]
            a[i] %= MOD
        self.__butterfly_inv(a)
        a = a[:n + m - 1]
        iz = pow(z, MOD - 2, MOD)
        for i in range(n + m - 1):
            a[i] *= iz
            a[i] %= MOD
        return a




def atcoder_practice2_f():
    import sys
    input = sys.stdin.buffer.readline

    N, M = map(int, input().split())
    A = [int(x) for x in input().split()]
    B = [int(x) for x in input().split()]

    convolution = Convolution(998244353)
    print(*convolution(A, B))


if __name__ == "__main__":
    atcoder_practice2_f()

Solution (Python):

MOD = None

class Convolution:

    
    def __init__(self, mod):
        global MOD
        MOD = mod
        

    def __butterfly(self, arr):
        n = len(arr)
        h = (n - 1).bit_length()
        
        sum_e = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 0, 0, 0, 0, 0, 0, 0, 0, 0)
        for ph in range(1, h + 1):
            w = 1 << (ph - 1)
            p = 1 << (h - ph)
            now = 1
            for s in range(w):
                offset = s << (h - ph + 1)
                for i in range(p):
                    l = arr[i + offset]
                    r = arr[i + offset + p] * now
                    arr[i + offset] = (l + r) % MOD
                    arr[i + offset + p] = (l - r) % MOD
                now *= sum_e[(~s & -~s).bit_length() - 1]
                now %= MOD

    def __butterfly_inv(self, arr):
        n = len(arr)
        h = (n - 1).bit_length()
        
        sum_ie = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543,
                  109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 0, 0, 0, 0, 0, 0, 0, 0, 0)
        for ph in range(1, h + 1)[::-1]:
            w = 1 << (ph - 1)
            p = 1 << (h - ph)
            inow = 1
            for s in range(w):
                offset = s << (h - ph + 1)
                for i in range(p):
                    l = arr[i + offset]
                    r = arr[i + offset + p]
                    arr[i + offset] = (l + r) % MOD
                    arr[i + offset + p] = (MOD + l - r) * inow % MOD
                inow *= sum_ie[(~s & -~s).bit_length() - 1]
                inow %= MOD

    def __call__(self, a, b):
        n = len(a)
        m = len(b)
        
        if not n or not m: return []
        if min(n, m) <= 50:
            if n < m:
                n, m = m, n
                a, b = b, a
            res = [0] * (n + m - 1)
            for i in range(n):
                for j in range(m):
                    res[i + j] += a[i] * b[j]
                    res[i + j] %= MOD
            return res
        z = 1 << (n + m - 2).bit_length()
        a += [0] * (z - n)
        b += [0] * (z - m)
        self.__butterfly(a)
        self.__butterfly(b)
        for i in range(z):
            a[i] *= b[i]
            a[i] %= MOD
        self.__butterfly_inv(a)
        a = a[:n + m - 1]
        iz = pow(z, MOD - 2, MOD)
        for i in range(n + m - 1):
            a[i] *= iz
            a[i] %= MOD
        return a




def atcoder_practice2_f():
    import sys
    input = sys.stdin.buffer.readline

    N, M = map(int, input().split())
    A = [int(x) for x in input().split()]
    B = [int(x) for x in input().split()]

    convolution = Convolution(998244353)
    print(*convolution(A, B))


if __name__ == "__main__":
    atcoder_practice2_f()