Buggy python submission (verdict: Time Limit Exceeded):
import sys
input = sys.stdin.readline
n,t = map(int,input().split())
data = [list(map(int,input().split())) for _ in range(n)]

dp1 = [[0 for i in range(n+1)] for j in range(t+1)]
dp2 = [[0 for i in range(n+1)] for j in range(t+1)]

q = 0
for i in range(1,n+1):
    q = max(q,data[i-1][0])
    dp2[1][i] = q

for i in range(1,t+1):
    for j in range(1,n+1):
        if i-data[j-1][0] >= 0:
            dp1[i][j] = max(dp1[i][j-1],dp1[i-data[j-1][0]][j-1]+data[j-1][1])
            dp2[i][j] = max(dp2[i][j-1],dp2[i-data[j-1][0]][j-1]+data[j-1][1],dp1[i-1][j-1]+data[j-1][1])
        else:
            dp1[i][j] = dp1[i][j-1]
            dp2[i][j] = max(dp2[i][j-1],dp1[i-1][j-1]+data[j-1][1])


print(dp2[t][n])

Fixed submission:
n,t = map(int,input().split())
data = [list(map(int,input().split())) for _ in range(n)]

dp1 = [[0 for i in range(n+1)] for j in range(t+1)]
dp2 = [[0 for i in range(n+1)] for j in range(t+1)]

q = 0
for i in range(1,n+1):
    q = max(q,data[i-1][0])
    dp2[1][i] = q

for i in range(1,t+1):
    for j in range(1,n+1):
        if i-data[j-1][0] >= 0:
            dp1[i][j] = max(dp1[i][j-1],dp1[i-data[j-1][0]][j-1]+data[j-1][1])
            dp2[i][j] = max(dp2[i][j-1],dp2[i-data[j-1][0]][j-1]+data[j-1][1],dp1[i-1][j-1]+data[j-1][1])
        else:
            dp1[i][j] = dp1[i][j-1]
            dp2[i][j] = max(dp2[i][j-1],dp1[i-1][j-1]+data[j-1][1])


print(dp2[t][n])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
input = sys.stdin.readline
N,T = map(int,input().split())
data = [list(map(int,input().split())) for _ in range(N)]

dp1 = [[0]*(N+1) for t in range(T+1)] #dp1[t][n] := (data[:n]の中からtまでに食べ切る範囲で美味しく）
dp2 = [[0]*(N+1) for t in range(T+1)] #dp1[t][n] := (data[:n]の中からt-1までに注文する範囲で美味しく)


for t in range(1,T+1):
    for n in range(1,N+1):
        if t-data[n-1][0] >= 0:
            dp1[t][n] = max(dp1[t][n-1],dp1[t-data[n-1][0]][n-1]+data[n-1][1])
            dp2[t][n] = max(dp2[t][n-1],dp2[t-data[n-1][0]][n-1]+data[n-1][1],dp1[t-1][n-1]+data[n-1][1])
        else:
            dp1[t][n] = dp1[t][n-1]
            dp2[t][n] = max(dp2[t][n-1],dp1[t-1][n-1]+data[n-1][1])


print(dp2[T][N])

Fixed submission:
n,t = map(int,input().split())
data = [list(map(int,input().split())) for _ in range(n)]

dp1 = [[0 for i in range(n+1)] for j in range(t+1)]
dp2 = [[0 for i in range(n+1)] for j in range(t+1)]

q = 0
for i in range(1,n+1):
    q = max(q,data[i-1][0])
    dp2[1][i] = q

for i in range(1,t+1):
    for j in range(1,n+1):
        if i-data[j-1][0] >= 0:
            dp1[i][j] = max(dp1[i][j-1],dp1[i-data[j-1][0]][j-1]+data[j-1][1])
            dp2[i][j] = max(dp2[i][j-1],dp2[i-data[j-1][0]][j-1]+data[j-1][1],dp1[i-1][j-1]+data[j-1][1])
        else:
            dp1[i][j] = dp1[i][j-1]
            dp2[i][j] = max(dp2[i][j-1],dp1[i-1][j-1]+data[j-1][1])


print(dp2[t][n])

Buggy python submission (verdict: Time Limit Exceeded):
N,T = map(int,input().split())
data = [list(map(int,input().split())) for _ in range(N)]

dp1 = [[0 for n in range(N+1)] for t in range(T+1)] #dp1[t][n] := (data[:n]の中からtまでに食べ切る範囲で美味しく）
dp2 = [[0 for n in range(N+1)] for t in range(T+1)] #dp1[t][n] := (data[:n]の中からt-1までに注文する範囲で美味しく)


for t in range(1,T+1):
    for n in range(1,N+1):
        if t-data[n-1][0] >= 0:
            dp1[t][n] = max(dp1[t][n-1],dp1[t-data[n-1][0]][n-1]+data[n-1][1])
            dp2[t][n] = max(dp2[t][n-1],dp2[t-data[n-1][0]][n-1]+data[n-1][1],dp1[t-1][n-1]+data[n-1][1])
        else:
            dp1[t][n] = dp1[t][n-1]
            dp2[t][n] = max(dp2[t][n-1],dp1[t-1][n-1]+data[n-1][1])


print(dp2[T][N])

Fixed submission:
n,t = map(int,input().split())
data = [list(map(int,input().split())) for _ in range(n)]

dp1 = [[0 for i in range(n+1)] for j in range(t+1)]
dp2 = [[0 for i in range(n+1)] for j in range(t+1)]

q = 0
for i in range(1,n+1):
    q = max(q,data[i-1][0])
    dp2[1][i] = q

for i in range(1,t+1):
    for j in range(1,n+1):
        if i-data[j-1][0] >= 0:
            dp1[i][j] = max(dp1[i][j-1],dp1[i-data[j-1][0]][j-1]+data[j-1][1])
            dp2[i][j] = max(dp2[i][j-1],dp2[i-data[j-1][0]][j-1]+data[j-1][1],dp1[i-1][j-1]+data[j-1][1])
        else:
            dp1[i][j] = dp1[i][j-1]
            dp2[i][j] = max(dp2[i][j-1],dp1[i-1][j-1]+data[j-1][1])


print(dp2[t][n])