Buggy python submission (verdict: Time Limit Exceeded):
n, k = map(int, input().split())
a = [int(x)-1 for x in input().split()]

inds = {}
y = [0]*n

for i in range(n):
    if a[i] in inds:
        y[inds[a[i]][-1]] = i+1 - inds[a[i]][-1]
        inds[a[i]].append(i)
    else:
        inds[a[i]] = [i]

for lst in inds.values():
    y[lst[-1]] = n+lst[0]+1 - lst[-1]

length = (n*k).bit_length()

db = [y]
for m in range(length):
    db.append([db[-1][i] + db[-1][(i+db[-1][i]) % n] for i in range(n)])

cur = 0
i = length

while cur < n*k:
    while i > -1 and cur + db[i][cur % n] > n*k:
        i -= 1
    if i == -1:
        break
    cur = cur + db[i][cur % n]

ans = []
while cur < n*k:
    if cur + db[0][cur % n] > n*k:
        ans.append(cur)
        cur += 1
    elif cur + db[0][cur % n] == n*k:
        break
    else:
        cur = cur + db[0][cur % n]

print(*map(lambda x: a[x % n]+1, ans))


Fixed submission:
from bisect import bisect_right
n, k = map(int, input().split())
a = [int(x) for x in input().split()]

d = {}
for i in range(n):
    if a[i] in d:
        d[a[i]].append(i)
    else:
        d[a[i]] = [i]


def simulate(k):
    if k == 0:
        return 0, []
    lap = 1
    res = [0]
    while True:
        s = res.pop()
        nxt = d[a[s]][bisect_right(d[a[s]], s) % len(d[a[s]])] + 1
        if nxt == n:
            if lap == k and s == n-1:
                res.append(s)
            if s == n-1:
                lap += 1
            return lap, res
        elif nxt <= s+1:
            if lap == k:
                res.append(s)
                if s == n-1:
                    return lap, res
                res.append(s+1)
                if s+1 == n-1:
                    return lap, res
            else:
                res.append(nxt)
                lap += 1
        else:  # s+1 < nxt
            s = nxt
            res.append(s)
    return 0


period, ans = simulate(k)

if period != k:
    lap, ans = simulate(k % period)

print(*[a[x] for x in ans])

Buggy python submission (verdict: Time Limit Exceeded):
n, k = map(int, input().split())
a = [int(x)-1 for x in input().split()]

inds = {}
y = [0]*n

for i in range(n):
    if a[i] in inds:
        y[inds[a[i]][-1]] = i+1 - inds[a[i]][-1]
        inds[a[i]].append(i)
    else:
        inds[a[i]] = [i]

for lst in inds.values():
    y[lst[-1]] = n+lst[0]+1 - lst[-1]

length = (n*k).bit_length()

db = {0: y}
for m in range(length):
    db[m+1] = [db[m][i] + db[m][(i+db[m][i]) % n] for i in range(n)]

cur = 0
i = length

while cur < n*k:
    while i > -1 and cur + db[i][cur % n] > n*k:
        i -= 1
    if i == -1:
        break
    cur = cur + db[i][cur % n]

ans = []
while cur < n*k:
    if cur + db[0][cur % n] > n*k:
        ans.append(cur)
        cur += 1
    elif cur + db[0][cur % n] == n*k:
        break
    else:
        cur = cur + db[0][cur % n]

print(*map(lambda x: a[x % n]+1, ans))


Fixed submission:
from bisect import bisect_right
n, k = map(int, input().split())
a = [int(x) for x in input().split()]

d = {}
for i in range(n):
    if a[i] in d:
        d[a[i]].append(i)
    else:
        d[a[i]] = [i]


def simulate(k):
    if k == 0:
        return 0, []
    lap = 1
    res = [0]
    while True:
        s = res.pop()
        nxt = d[a[s]][bisect_right(d[a[s]], s) % len(d[a[s]])] + 1
        if nxt == n:
            if lap == k and s == n-1:
                res.append(s)
            if s == n-1:
                lap += 1
            return lap, res
        elif nxt <= s+1:
            if lap == k:
                res.append(s)
                if s == n-1:
                    return lap, res
                res.append(s+1)
                if s+1 == n-1:
                    return lap, res
            else:
                res.append(nxt)
                lap += 1
        else:  # s+1 < nxt
            s = nxt
            res.append(s)
    return 0


period, ans = simulate(k)

if period != k:
    lap, ans = simulate(k % period)

print(*[a[x] for x in ans])

Buggy python submission (verdict: Time Limit Exceeded):
n, k = map(int, input().split())
a = [int(x)-1 for x in input().split()]

inds = {}
y = [0]*n

for i in range(n):
    if a[i] in inds:
        y[inds[a[i]][-1]] = i+1 - inds[a[i]][-1]
        inds[a[i]].append(i)
    else:
        inds[a[i]] = [i]

for lst in inds.values():
    y[lst[-1]] = n+lst[0]+1 - lst[-1]

length = (n*k).bit_length()

db = [y]
for m in range(length):
    next_y = [0]*n
    for i in range(n):
        next_y[i] = db[-1][i] + db[-1][(i+db[-1][i]) % n]
    db.append(next_y)

cur = 0
i = length

while cur < n*k:
    while i > -1 and cur + db[i][cur % n] > n*k:
        i -= 1
    if i == -1:
        break
    cur = cur + db[i][cur % n]

ans = []
while cur < n*k:
    if cur + db[0][cur % n] > n*k:
        ans.append(cur)
        cur += 1
    elif cur + db[0][cur % n] == n*k:
        break
    else:
        cur = cur + db[0][cur % n]

print(*map(lambda x: a[x % n]+1, ans))


Fixed submission:
from bisect import bisect_right
n, k = map(int, input().split())
a = [int(x) for x in input().split()]

d = {}
for i in range(n):
    if a[i] in d:
        d[a[i]].append(i)
    else:
        d[a[i]] = [i]


def simulate(k):
    if k == 0:
        return 0, []
    lap = 1
    res = [0]
    while True:
        s = res.pop()
        nxt = d[a[s]][bisect_right(d[a[s]], s) % len(d[a[s]])] + 1
        if nxt == n:
            if lap == k and s == n-1:
                res.append(s)
            if s == n-1:
                lap += 1
            return lap, res
        elif nxt <= s+1:
            if lap == k:
                res.append(s)
                if s == n-1:
                    return lap, res
                res.append(s+1)
                if s+1 == n-1:
                    return lap, res
            else:
                res.append(nxt)
                lap += 1
        else:  # s+1 < nxt
            s = nxt
            res.append(s)
    return 0


period, ans = simulate(k)

if period != k:
    lap, ans = simulate(k % period)

print(*[a[x] for x in ans])

Buggy python submission (verdict: Time Limit Exceeded):
n, k = map(int, input().split())
a = [int(x)-1 for x in input().split()]

inds = [[] for _ in range(max(a)+1)]
y = [0]*n

for i in range(n):
    if inds[a[i]]:
        y[inds[a[i]][-1]] = i+1 - inds[a[i]][-1]
    inds[a[i]].append(i)

for j in range(max(a)+1):
    if inds[j]:
        y[inds[j][-1]] = n+inds[j][0]+1 - inds[j][-1]

length = (n*k*2).bit_length()

db = [y]
for m in range(length):
    next_y = [0]*n
    for i in range(n):
        next_y[i] = db[-1][i] + db[-1][(i+db[-1][i]) % n]
    db.append(next_y)


def last():
    cur = 0
    while True:
        for i in range(length+1):
            if cur + db[i][cur % n] > n*k:
                if i != 0:
                    cur += db[i-1][cur % n]
                    break
                else:
                    return cur


cur = last()

ans = []
while cur < n*k:
    if cur + db[0][cur % n] > n*k:
        ans.append(cur)
        cur += 1
    elif cur + db[0][cur % n] == n*k:
        break
    else:
        cur = cur + db[0][cur % n]

print(*map(lambda x: a[x % n]+1, ans))


Fixed submission:
from bisect import bisect_right
n, k = map(int, input().split())
a = [int(x) for x in input().split()]

d = {}
for i in range(n):
    if a[i] in d:
        d[a[i]].append(i)
    else:
        d[a[i]] = [i]


def simulate(k):
    if k == 0:
        return 0, []
    lap = 1
    res = [0]
    while True:
        s = res.pop()
        nxt = d[a[s]][bisect_right(d[a[s]], s) % len(d[a[s]])] + 1
        if nxt == n:
            if lap == k and s == n-1:
                res.append(s)
            if s == n-1:
                lap += 1
            return lap, res
        elif nxt <= s+1:
            if lap == k:
                res.append(s)
                if s == n-1:
                    return lap, res
                res.append(s+1)
                if s+1 == n-1:
                    return lap, res
            else:
                res.append(nxt)
                lap += 1
        else:  # s+1 < nxt
            s = nxt
            res.append(s)
    return 0


period, ans = simulate(k)

if period != k:
    lap, ans = simulate(k % period)

print(*[a[x] for x in ans])

Buggy python submission (verdict: Time Limit Exceeded):
n, k = map(int, input().split())
a = [int(x)-1 for x in input().split()]

inds = [[] for _ in range(max(a)+1)]
y = [0]*n

for i in range(n):
    if inds[a[i]]:
        y[inds[a[i]][-1]] = i+1 - inds[a[i]][-1]
    inds[a[i]].append(i)

for j in range(max(a)+1):
    if inds[j]:
        y[inds[j][-1]] = n+inds[j][0]+1 - inds[j][-1]

length = (n*k).bit_length()

db = [y]
for m in range(length):
    next_y = [0]*n
    for i in range(n):
        next_y[i] = db[-1][i] + db[-1][(i+db[-1][i]) % n]
    db.append(next_y)


def last():
    cur = 0
    while True:
        for i in range(length+1):
            if cur + db[i][cur % n] > n*k:
                if i != 0:
                    cur += db[i-1][cur % n]
                    break
                else:
                    return cur


cur = last()

ans = []
while cur < n*k:
    if cur + db[0][cur % n] > n*k:
        ans.append(cur)
        cur += 1
    elif cur + db[0][cur % n] == n*k:
        break
    else:
        cur = cur + db[0][cur % n]

print(*map(lambda x: a[x % n]+1, ans))


Fixed submission:
from bisect import bisect_right
n, k = map(int, input().split())
a = [int(x) for x in input().split()]

d = {}
for i in range(n):
    if a[i] in d:
        d[a[i]].append(i)
    else:
        d[a[i]] = [i]


def simulate(k):
    if k == 0:
        return 0, []
    lap = 1
    res = [0]
    while True:
        s = res.pop()
        nxt = d[a[s]][bisect_right(d[a[s]], s) % len(d[a[s]])] + 1
        if nxt == n:
            if lap == k and s == n-1:
                res.append(s)
            if s == n-1:
                lap += 1
            return lap, res
        elif nxt <= s+1:
            if lap == k:
                res.append(s)
                if s == n-1:
                    return lap, res
                res.append(s+1)
                if s+1 == n-1:
                    return lap, res
            else:
                res.append(nxt)
                lap += 1
        else:  # s+1 < nxt
            s = nxt
            res.append(s)
    return 0


period, ans = simulate(k)

if period != k:
    lap, ans = simulate(k % period)

print(*[a[x] for x in ans])

Buggy python submission (verdict: Time Limit Exceeded):
n, k = map(int, input().split())
a = [int(x)-1 for x in input().split()]

inds = [[] for _ in range(max(a)+1)]
y = [0]*n

for i in range(n):
    if inds[a[i]]:
        y[inds[a[i]][-1]] = i+1 - inds[a[i]][-1]
    inds[a[i]].append(i)

for j in range(max(a)+1):
    if inds[j]:
        y[inds[j][-1]] = n+inds[j][0]+1 - inds[j][-1]

length = (n*k).bit_length()

db = [y]
for m in range(length):
    next_y = [0]*n
    for i in range(n):
        next_y[i] = db[-1][i] + db[-1][(i+db[-1][i]) % n]
    db.append(next_y)

cur = 0
i = length

while cur < n*k:
    while i > -1 and cur + db[i][cur % n] > n*k:
        i -= 1
    if i == -1:
        break
    cur = cur + db[i][cur % n]

ans = []
while cur < n*k:
    if cur + db[0][cur % n] > n*k:
        ans.append(cur)
        cur += 1
    elif cur + db[0][cur % n] == n*k:
        break
    else:
        cur = cur + db[0][cur % n]

print(*map(lambda x: a[x % n]+1, ans))


Fixed submission:
from bisect import bisect_right
n, k = map(int, input().split())
a = [int(x) for x in input().split()]

d = {}
for i in range(n):
    if a[i] in d:
        d[a[i]].append(i)
    else:
        d[a[i]] = [i]


def simulate(k):
    if k == 0:
        return 0, []
    lap = 1
    res = [0]
    while True:
        s = res.pop()
        nxt = d[a[s]][bisect_right(d[a[s]], s) % len(d[a[s]])] + 1
        if nxt == n:
            if lap == k and s == n-1:
                res.append(s)
            if s == n-1:
                lap += 1
            return lap, res
        elif nxt <= s+1:
            if lap == k:
                res.append(s)
                if s == n-1:
                    return lap, res
                res.append(s+1)
                if s+1 == n-1:
                    return lap, res
            else:
                res.append(nxt)
                lap += 1
        else:  # s+1 < nxt
            s = nxt
            res.append(s)
    return 0


period, ans = simulate(k)

if period != k:
    lap, ans = simulate(k % period)

print(*[a[x] for x in ans])