Buggy python submission (verdict: Time Limit Exceeded):
import sys

read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines
sys.setrecursionlimit(10 ** 9)
INF = 1 << 60
MOD = 1000000007


def main():
    N, T, *AB = map(int, read().split())
    D = [(a, b) for a, b in zip(*[iter(AB)] * 2)]

    D.sort()

    dp = [0] * T
    ans = 0

    for i in range(N - 1):
        for t in range(T - 1, -1, -1):
            if t - D[i][0] >= 0 and dp[t] < dp[t - D[i][0]] + D[i][1]:
                dp[t] = dp[t - D[i][0]] + D[i][1]
        if ans < dp[T - 1] + D[i + 1][1]:
            ans = dp[T - 1] + D[i + 1][1]

    print(ans)
    return


if __name__ == '__main__':
    main()


Fixed submission:
import sys

read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines
sys.setrecursionlimit(10 ** 9)
INF = 1 << 60
MOD = 1000000007


def main():
    N, T, *AB = map(int, read().split())
    A = AB[::2]
    B = AB[1::2]

    dp1 = [[0] * T for _ in range(N + 1)]
    for i in range(N):
        for t in range(T):
            if 0 <= t - A[i]:
                dp1[i + 1][t] = dp1[i][t - A[i]] + B[i]
            if dp1[i + 1][t] < dp1[i][t]:
                dp1[i + 1][t] = dp1[i][t]

    dp2 = [[0] * T for _ in range(N + 1)]
    for i in range(N - 1, -1, -1):
        for t in range(T):
            if 0 <= t - A[i]:
                dp2[i][t] = dp2[i + 1][t - A[i]] + B[i]
            if dp2[i][t] < dp2[i + 1][t]:
                dp2[i][t] = dp2[i + 1][t]

    ans = 0
    for i in range(N):
        tmp = max(dp1[i][t] + dp2[i + 1][T - t - 1] for t in range(T)) + B[i]
        if ans < tmp:
            ans = tmp

    print(ans)
    return


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
import sys

read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines
sys.setrecursionlimit(10 ** 9)
INF = 1 << 60
MOD = 1000000007


def main():
    N, T, *AB = map(int, read().split())
    D = [(a, b) for a, b in zip(*[iter(AB)] * 2)]

    D.sort()

    dp = [[0] * T for _ in range(N + 1)]

    for i in range(N):
        for t in range(T):
            if t - D[i][0] >= 0:
                dp[i + 1][t] = dp[i][t - D[i][0]] + D[i][1]
            if dp[i + 1][t] < dp[i][t]:
                dp[i + 1][t] = dp[i][t]

    ans = 0
    for i in range(N):
        if ans < dp[i][T - 1] + D[i][1]:
            ans = dp[i][T - 1] + D[i][1]

    print(ans)
    return


if __name__ == '__main__':
    main()


Fixed submission:
import sys

read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines
sys.setrecursionlimit(10 ** 9)
INF = 1 << 60
MOD = 1000000007


def main():
    N, T, *AB = map(int, read().split())
    A = AB[::2]
    B = AB[1::2]

    dp1 = [[0] * T for _ in range(N + 1)]
    for i in range(N):
        for t in range(T):
            if 0 <= t - A[i]:
                dp1[i + 1][t] = dp1[i][t - A[i]] + B[i]
            if dp1[i + 1][t] < dp1[i][t]:
                dp1[i + 1][t] = dp1[i][t]

    dp2 = [[0] * T for _ in range(N + 1)]
    for i in range(N - 1, -1, -1):
        for t in range(T):
            if 0 <= t - A[i]:
                dp2[i][t] = dp2[i + 1][t - A[i]] + B[i]
            if dp2[i][t] < dp2[i + 1][t]:
                dp2[i][t] = dp2[i + 1][t]

    ans = 0
    for i in range(N):
        tmp = max(dp1[i][t] + dp2[i + 1][T - t - 1] for t in range(T)) + B[i]
        if ans < tmp:
            ans = tmp

    print(ans)
    return


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
import sys

read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines
sys.setrecursionlimit(10 ** 9)
INF = 1 << 60
MOD = 1000000007


def main():
    N, T, *AB = map(int, read().split())
    A = AB[::2]
    B = AB[1::2]

    dp = [[0] * T for _ in range(N + 1)]
    for i in range(N):
        for t in range(T):
            if 0 <= t - A[i]:
                dp[i + 1][t] = dp[i][t - A[i]] + B[i]
            if dp[i + 1][t] < dp[i][t]:
                dp[i + 1][t] = dp[i][t]

    C = [False] * N

    t = T - 1
    for i in range(N - 1, -1, -1):
        if dp[i + 1][t] == dp[i][t - A[i]] + B[i]:
            C[i] = True
            t -= A[i]

    ans = dp[N][T - 1] + max((B[i] for i in range(N) if not C[i]), default=0)

    print(ans)
    return


if __name__ == '__main__':
    main()


Fixed submission:
import sys

read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines
sys.setrecursionlimit(10 ** 9)
INF = 1 << 60
MOD = 1000000007


def main():
    N, T, *AB = map(int, read().split())
    A = AB[::2]
    B = AB[1::2]

    dp1 = [[0] * T for _ in range(N + 1)]
    for i in range(N):
        for t in range(T):
            if 0 <= t - A[i]:
                dp1[i + 1][t] = dp1[i][t - A[i]] + B[i]
            if dp1[i + 1][t] < dp1[i][t]:
                dp1[i + 1][t] = dp1[i][t]

    dp2 = [[0] * T for _ in range(N + 1)]
    for i in range(N - 1, -1, -1):
        for t in range(T):
            if 0 <= t - A[i]:
                dp2[i][t] = dp2[i + 1][t - A[i]] + B[i]
            if dp2[i][t] < dp2[i + 1][t]:
                dp2[i][t] = dp2[i + 1][t]

    ans = 0
    for i in range(N):
        tmp = max(dp1[i][t] + dp2[i + 1][T - t - 1] for t in range(T)) + B[i]
        if ans < tmp:
            ans = tmp

    print(ans)
    return


if __name__ == '__main__':
    main()