Buggy python submission (verdict: Time Limit Exceeded):
def main():
    s = input()
    n = len(s)
    k = int(input())
    # dp[使った回数][左端からの距離][左端]
    dp = [[[1]*(n-i) for i in range(n)] for _ in range(k+1)]

    if n == 1:
        print(1)
        return
    dp2 = dp[0][1]
    for i in range(n-1):
        if s[i] == s[i+1]:
            dp2[i] = 2
    if k > 0:
        for cnt in range(1, k+1):
            dp2 = dp[cnt][1]
            for i in range(n-1):
                dp2[i] = 2

    for cnt in range(k):
        dp2 = dp[cnt]
        dp4 = dp[cnt+1]
        for d in range(2, n):
            dp3 = dp2[d]
            dp5 = dp2[d-1]
            dp6 = dp2[d-2]
            dp7 = dp4[d]
            for left in range(n-d):
                right = left+d
                plus = (s[left] == s[right])*2
                dp3[left] = max(
                    dp3[left], dp5[left],
                    dp5[left+1], dp6[left+1]+plus)
                dp7[left] = max(
                    dp7[left], dp3[left], dp6[left+1]+2)
    dp2 = dp[k]
    for d in range(2, n):
        dp3 = dp2[d]
        dp4 = dp2[d-1]
        dp5 = dp2[d-2]
        for left in range(n-d):
            right = left+d
            plus = (s[left] == s[right])*2
            dp3[left] = max(
                dp3[left], dp4[left], dp4[left+1], dp5[left+1]+plus)
    print(dp[-1][-1][0])


main()


Fixed submission:
def main():
    s = input()
    n = len(s)
    k = int(input())
    # dp[使った回数][左端からの距離][左端]
    dp = [[[1]*(n-i) for i in range(n)] for _ in range(k+1)]

    for i in range(n-1):
        if s[i] == s[i+1]:
            dp[0][1][i] = 2
    if k > 0:
        for cnt in range(1, k+1):
            for i in range(n-1):
                dp[cnt][1][i] = 2

    for cnt in range(k):
        for d in range(2, n):
            for left in range(n-d):
                right = left+d
                plus = (s[left] == s[right])*2
                dp[cnt][d][left] = max(
                    dp[cnt][d][left], dp[cnt][d-1][left],
                    dp[cnt][d-1][left+1], dp[cnt][d-2][left+1]+plus)
                dp[cnt+1][d][left] = max(
                    dp[cnt+1][d][left], dp[cnt][d][left], dp[cnt][d-2][left+1]+2)
    for d in range(2, n):
        for left in range(n-d):
            right = left+d
            plus = (s[left] == s[right])*2
            dp[k][d][left] = max(
                dp[k][d][left], dp[k][d-1][left], dp[k][d-1][left+1], dp[k][d-2][left+1]+plus)
    print(dp[-1][-1][0])


main()

Buggy python submission (verdict: Runtime Error):
def main():
    s = input()
    n = len(s)
    k = int(input())
    # dp[使った回数][左端からの距離][左端]
    dp = [[[1]*(n-i) for i in range(n)] for _ in range(k+1)]

    dp2 = dp[0][1]
    for i in range(n-1):
        if s[i] == s[i+1]:
            dp2[i] = 2
    if k > 0:
        for cnt in range(1, k+1):
            dp2 = dp[cnt][1]
            for i in range(n-1):
                dp2[i] = 2

    for cnt in range(k):
        dp2 = dp[cnt]
        for d in range(2, n):
            dp3 = dp2[d]
            for left in range(n-d):
                right = left+d
                plus = (s[left] == s[right])*2
                dp3[left] = max(
                    dp3[left], dp2[d-1][left],
                    dp2[d-1][left+1], dp2[d-2][left+1]+plus)
                dp[cnt+1][d][left] = max(
                    dp[cnt+1][d][left], dp3[left], dp2[d-2][left+1]+2)
    dp2 = dp[k]
    for d in range(2, n):
        dp3 = dp[d]
        for left in range(n-d):
            right = left+d
            plus = (s[left] == s[right])*2
            dp3[left] = max(
                dp3[left], dp2[d-1][left], dp2[d-1][left+1], dp2[d-2][left+1]+plus)
    print(dp[-1][-1][0])


main()

Fixed submission:
def main():
    s = input()
    n = len(s)
    k = int(input())
    # dp[使った回数][左端からの距離][左端]
    dp = [[[1]*(n-i) for i in range(n)] for _ in range(k+1)]

    for i in range(n-1):
        if s[i] == s[i+1]:
            dp[0][1][i] = 2
    if k > 0:
        for cnt in range(1, k+1):
            for i in range(n-1):
                dp[cnt][1][i] = 2

    for cnt in range(k):
        for d in range(2, n):
            for left in range(n-d):
                right = left+d
                plus = (s[left] == s[right])*2
                dp[cnt][d][left] = max(
                    dp[cnt][d][left], dp[cnt][d-1][left],
                    dp[cnt][d-1][left+1], dp[cnt][d-2][left+1]+plus)
                dp[cnt+1][d][left] = max(
                    dp[cnt+1][d][left], dp[cnt][d][left], dp[cnt][d-2][left+1]+2)
    for d in range(2, n):
        for left in range(n-d):
            right = left+d
            plus = (s[left] == s[right])*2
            dp[k][d][left] = max(
                dp[k][d][left], dp[k][d-1][left], dp[k][d-1][left+1], dp[k][d-2][left+1]+plus)
    print(dp[-1][-1][0])


main()

Buggy python submission (verdict: Time Limit Exceeded):
def main():
    s = input()
    n = len(s)
    k = int(input())
    # dp[左端][左端からの右端の距離][使った回数]
    dp = [[[1]*(k+1) for _ in [0]*(n-i)] for i in range(n)]

    for i in range(n-1):
        if s[i] == s[i+1]:
            dp[i][1][0] = 2
    if k > 0:
        for cnt in range(1, k+1):
            for i in range(n-1):
                dp[i][1][cnt] = 2

    for cnt in range(k):
        for d in range(2, n):
            for left in range(n-d):
                right = left+d
                plus = (s[left] == s[right])*2
                dp[left][d][cnt] = max(
                    dp[left][d][cnt], dp[left][d-1][cnt],
                    dp[left+1][d-1][cnt], dp[left+1][d-2][cnt]+plus)
                dp[left][d][cnt+1] = max(
                    max(dp[left][d][cnt:cnt+2]), dp[left+1][d-2][cnt]+2)
    for d in range(2, n):
        for left in range(n-d):
            right = left+d
            plus = (s[left] == s[right])*2
            dp[left][d][k] = max(
                dp[left][d][k], dp[left][d-1][k], dp[left+1][d-1][k], dp[left+1][d-2][k]+plus)
    print(dp[0][-1][-1])


main()

Fixed submission:
def main():
    s = input()
    n = len(s)
    k = int(input())
    # dp[使った回数][左端からの距離][左端]
    dp = [[[1]*(n-i) for i in range(n)] for _ in range(k+1)]

    for i in range(n-1):
        if s[i] == s[i+1]:
            dp[0][1][i] = 2
    if k > 0:
        for cnt in range(1, k+1):
            for i in range(n-1):
                dp[cnt][1][i] = 2

    for cnt in range(k):
        for d in range(2, n):
            for left in range(n-d):
                right = left+d
                plus = (s[left] == s[right])*2
                dp[cnt][d][left] = max(
                    dp[cnt][d][left], dp[cnt][d-1][left],
                    dp[cnt][d-1][left+1], dp[cnt][d-2][left+1]+plus)
                dp[cnt+1][d][left] = max(
                    dp[cnt+1][d][left], dp[cnt][d][left], dp[cnt][d-2][left+1]+2)
    for d in range(2, n):
        for left in range(n-d):
            right = left+d
            plus = (s[left] == s[right])*2
            dp[k][d][left] = max(
                dp[k][d][left], dp[k][d-1][left], dp[k][d-1][left+1], dp[k][d-2][left+1]+plus)
    print(dp[-1][-1][0])


main()