Problem p02862 (python)

Fixed submission:
from collections import Counter,defaultdict,deque
from heapq import heappop,heappush,heapify
import sys,bisect,math,itertools
sys.setrecursionlimit(10**8)
mod = 10**9+7
mod2 = 998244353
INF = float('inf')
def inp(): return int(sys.stdin.readline())
def inpl(): return list(map(int, sys.stdin.readline().split()))
def inpln(n): return list(int(sys.stdin.readline()) for i in range(n))

# def conb(n,r): 
#     return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))

x,y = inpl()
x,y = max(x,y),min(x,y)
if (x+y)%3 or y*2 < x:
    print(0)
    quit()
n = (x+y)//3 + 1
k = x-n+2


def cmd(n,r):
    if n - r < r: r = n - r
    if r == 0: return 1
    if r == 1: return n

    numerator = [n - r + k + 1 for k in range(r)]
    denominator = [k + 1 for k in range(r)]

    for p in range(2,r+1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p
            for k in range(p-1,r,p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot

    result = 1
    for k in range(r):
        if numerator[k] > 1:
            result *= int(numerator[k])

    return result

a = cmd(n-1,k-1)%mod
print(a)

Buggy submission (verdict: Runtime Error):
from collections import Counter,defaultdict,deque
from heapq import heappop,heappush,heapify
import sys,bisect,math,itertools
sys.setrecursionlimit(10**8)
mod = 10**9+7
mod2 = 998244353
INF = float('inf')
def inp(): return int(sys.stdin.readline())
def inpl(): return list(map(int, sys.stdin.readline().split()))
def inpln(n): return list(int(sys.stdin.readline()) for i in range(n))

n,w = inpl()
wv = [inpl() for i in range(n)]
dp = [[0 for i in range(w+1)] for j in range(n+1)]
wv.sort()
wv.sort(key=lambda x:x[1])
ww = [0] * n
vv = [0] * n
for i in range(n):
    ww[i],vv[i] = wv[i][0], wv[i][1]
for i in range(n-1):
    for j in range(w+1):
        if j >= ww[i]:
            dp[i+1][j] = max(dp[i][j], dp[i][j-ww[i]]+vv[i])
        else:
            dp[i+1][j] = dp[i][j]
res = dp[n-1][w-1]+wv[n-1][1]
tmp = wv[n-1][1]
dp = [[0 for i in range(w+1)] for j in range(n+1)]
wv.sort()
ww = [0] * n
vv = [0] * n
for i in range(n):
    ww[i],vv[i] = wv[i][0], wv[i][1]

if sum(ww[:n-1]) < w:
    print(sum(vv))
    quit()
for i in range(n-1):
    for j in range(w+1):
        if j >= ww[i]:
            dp[i+1][j] = max(dp[i][j], dp[i][j-ww[i]]+vv[i])
        else:
            dp[i+1][j] = dp[i][j]
print(max(res,dp[n-1][w-1]+tmp))

Buggy submission (verdict: Runtime Error):
from collections import Counter,defaultdict,deque
from heapq import heappop,heappush,heapify
import sys,bisect,math,itertools
sys.setrecursionlimit(10**8)
mod = 10**9+7
mod2 = 998244353
INF = float('inf')
def inp(): return int(sys.stdin.readline())
def inpl(): return list(map(int, sys.stdin.readline().split()))
def inpln(n): return list(int(sys.stdin.readline()) for i in range(n))

# def conb(n,r): 
#     return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
from scipy.special import comb
x,y = inpl()
x,y = max(x,y),min(x,y)
if (x+y)%3 or y*2 < x:
    print(0)
    quit()
n = (x+y)//3 + 1
k = x-n+2


def cmd(n,r):
    if n - r < r: r = n - r
    if r == 0: return 1
    if r == 1: return n

    numerator = [n - r + k + 1 for k in range(r)]
    denominator = [k + 1 for k in range(r)]

    for p in range(2,r+1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p
            for k in range(p-1,r,p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot

    result = 1
    for k in range(r):
        if numerator[k] > 1:
            result *= int(numerator[k])

    return result

a = cmd(n-1,k-1)%mod
print(a)