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

N, W = map(int, input().split())
WV = [list(map(int, sys.stdin.readline().split())) for i in range(N)]

INF = 10**10 + 1
dp = [[INF]*(N+1) for i in range(1000*N+2)]

for i in range(N+1):
        dp[0][i]=0

i = 1

while(True):
        for j in range(1, N+1):
                if i-WV[j-1][1]>=0:
                        dp[i][j] = min(dp[i-WV[j-1][1]][j-1]+WV[j-1][0], dp[i][j-1])
                else:
                        dp[i][j] = min(dp[i][j-1], WV[j-1][0])
        #print(i, dp[i][N])
        if dp[i-1][N] <= W and dp[i][N] > W:
                break
        i += 1

print(i-1)

Fixed submission:
import sys

N, W = map(int, input().split())
WV = [list(map(int, sys.stdin.readline().split())) for i in range(N)]
'''
w = [0]*N
v = [0]*N
for i in range(N):
        w[i], v[i] = map(int, sys.stdin.readline().split())
'''
INF = 10**11+1
dp = [[INF]*(N+1) for j in range(N*(10**3)+10)]
i = 1
ans = INF
while(True):
        for j in range(1, N+1):
                #print(i, j)
                w = WV[j-1][1]
                if i-w > 0:
                        dp[i][j] = min(dp[i][j-1], dp[i-w][j-1]+WV[j-1][0])
                        #dp[i][j] = max(dp[i-WV[j-1][0]][j-1]+WV[j-1][1], dp[i][j-1])
                else:
                        dp[i][j] = min(dp[i][j-1], WV[j-1][0])
        #print(dp[i][N])
        #print(i, dp[i][N])
        if dp[i][N] > W and ans <= W:
                print(i-1)
                exit()
        ans = dp[i][N]
        '''
        if dp[i][N] >= W:
                if ans == 0:
                        ans = dp[i][N]
                elif ans < dp[i][N]:
                        print(i)
                        exit()
                print(i, ans)
        '''
        i += 1

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

N, W = map(int, input().split())
WV = [list(map(int, sys.stdin.readline().split())) for i in range(N)]

INF = 10**10 + 1
dp = [[INF]*(N+1) for i in range(1000*N+1)]

for i in range(N+1):
        dp[0][i]=0

i = 1

while(True):
        for j in range(1, N+1):
                if i-WV[j-1][1]>=0:
                        dp[i][j] = min(dp[i-WV[j-1][1]][j-1]+WV[j-1][0], dp[i][j-1])
                else:
                        dp[i][j] = min(dp[i][j-1], WV[j-1][0])
        #print(i, dp[i][N])
        if dp[i-1][N] <= W and dp[i][N] > W:
                break
        i += 1

print(i-1)

Fixed submission:
import sys

N, W = map(int, input().split())
WV = [list(map(int, sys.stdin.readline().split())) for i in range(N)]
'''
w = [0]*N
v = [0]*N
for i in range(N):
        w[i], v[i] = map(int, sys.stdin.readline().split())
'''
INF = 10**11+1
dp = [[INF]*(N+1) for j in range(N*(10**3)+10)]
i = 1
ans = INF
while(True):
        for j in range(1, N+1):
                #print(i, j)
                w = WV[j-1][1]
                if i-w > 0:
                        dp[i][j] = min(dp[i][j-1], dp[i-w][j-1]+WV[j-1][0])
                        #dp[i][j] = max(dp[i-WV[j-1][0]][j-1]+WV[j-1][1], dp[i][j-1])
                else:
                        dp[i][j] = min(dp[i][j-1], WV[j-1][0])
        #print(dp[i][N])
        #print(i, dp[i][N])
        if dp[i][N] > W and ans <= W:
                print(i-1)
                exit()
        ans = dp[i][N]
        '''
        if dp[i][N] >= W:
                if ans == 0:
                        ans = dp[i][N]
                elif ans < dp[i][N]:
                        print(i)
                        exit()
                print(i, ans)
        '''
        i += 1