text stringlengths 198 433k | conversation_id int64 0 109k |
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider a tree (that is, an undirected connected graph without loops) T_1 and a tree T_2. Let's define their cartesian product T_1 × T_2 in a following way.
Let V be the set of vertices in T_1 and U be the set of vertices in T_2.
Then the set of vertices of graph T_1 × T_2 is V × U, that is, a set of ordered pairs of vertices, where the first vertex in pair is from V and the second — from U.
Let's draw the following edges:
* Between (v, u_1) and (v, u_2) there is an undirected edge, if u_1 and u_2 are adjacent in U.
* Similarly, between (v_1, u) and (v_2, u) there is an undirected edge, if v_1 and v_2 are adjacent in V.
Please see the notes section for the pictures of products of trees in the sample tests.
Let's examine the graph T_1 × T_2. How much cycles (not necessarily simple) of length k it contains? Since this number can be very large, print it modulo 998244353.
The sequence of vertices w_1, w_2, ..., w_k, where w_i ∈ V × U called cycle, if any neighboring vertices are adjacent and w_1 is adjacent to w_k. Cycles that differ only by the cyclic shift or direction of traversal are still considered different.
Input
First line of input contains three integers — n_1, n_2 and k (2 ≤ n_1, n_2 ≤ 4000, 2 ≤ k ≤ 75) — number of vertices in the first tree, number of vertices in the second tree and the cycle length respectively.
Then follow n_1 - 1 lines describing the first tree. Each of this lines contains two integers — v_i, u_i (1 ≤ v_i, u_i ≤ n_1), which define edges of the first tree.
Then follow n_2 - 1 lines, which describe the second tree in the same format.
It is guaranteed, that given graphs are trees.
Output
Print one integer — number of cycles modulo 998244353.
Examples
Input
2 2 2
1 2
1 2
Output
8
Input
2 2 4
1 2
1 2
Output
32
Input
2 3 4
1 2
1 2
1 3
Output
70
Input
4 2 2
1 2
1 3
1 4
1 2
Output
20
Note
The following three pictures illustrate graph, which are products of the trees from sample tests.
In the first example, the list of cycles of length 2 is as follows:
* «AB», «BA»
* «BC», «CB»
* «AD», «DA»
* «CD», «DC»
<image> <image> <image>
Submitted Solution:
```
print("big ppp")
```
No
| 84,800 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider a tree (that is, an undirected connected graph without loops) T_1 and a tree T_2. Let's define their cartesian product T_1 × T_2 in a following way.
Let V be the set of vertices in T_1 and U be the set of vertices in T_2.
Then the set of vertices of graph T_1 × T_2 is V × U, that is, a set of ordered pairs of vertices, where the first vertex in pair is from V and the second — from U.
Let's draw the following edges:
* Between (v, u_1) and (v, u_2) there is an undirected edge, if u_1 and u_2 are adjacent in U.
* Similarly, between (v_1, u) and (v_2, u) there is an undirected edge, if v_1 and v_2 are adjacent in V.
Please see the notes section for the pictures of products of trees in the sample tests.
Let's examine the graph T_1 × T_2. How much cycles (not necessarily simple) of length k it contains? Since this number can be very large, print it modulo 998244353.
The sequence of vertices w_1, w_2, ..., w_k, where w_i ∈ V × U called cycle, if any neighboring vertices are adjacent and w_1 is adjacent to w_k. Cycles that differ only by the cyclic shift or direction of traversal are still considered different.
Input
First line of input contains three integers — n_1, n_2 and k (2 ≤ n_1, n_2 ≤ 4000, 2 ≤ k ≤ 75) — number of vertices in the first tree, number of vertices in the second tree and the cycle length respectively.
Then follow n_1 - 1 lines describing the first tree. Each of this lines contains two integers — v_i, u_i (1 ≤ v_i, u_i ≤ n_1), which define edges of the first tree.
Then follow n_2 - 1 lines, which describe the second tree in the same format.
It is guaranteed, that given graphs are trees.
Output
Print one integer — number of cycles modulo 998244353.
Examples
Input
2 2 2
1 2
1 2
Output
8
Input
2 2 4
1 2
1 2
Output
32
Input
2 3 4
1 2
1 2
1 3
Output
70
Input
4 2 2
1 2
1 3
1 4
1 2
Output
20
Note
The following three pictures illustrate graph, which are products of the trees from sample tests.
In the first example, the list of cycles of length 2 is as follows:
* «AB», «BA»
* «BC», «CB»
* «AD», «DA»
* «CD», «DC»
<image> <image> <image>
Submitted Solution:
```
print("big pp")
```
No
| 84,801 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has X+Y balls. X of them have an integer A written on them, and the other Y of them have an integer B written on them.
Snuke will divide these balls into some number of groups. Here, every ball should be contained in exactly one group, and every group should contain one or more balls.
A group is said to be good when the sum of the integers written on the balls in that group is a multiple of an integer C. Find the maximum possible number of good groups.
Solve T test cases for each input file.
Constraints
* 1 \leq T \leq 2 \times 10^4
* 1 \leq A,X,B,Y,C \leq 10^9
* A \neq B
Input
Input is given from Standard Input in the following format. The first line is as follows:
T
Then, T test cases follow. Each test case is given in the following format:
A X B Y C
Output
For each test case, print a line containing the maximum possible number of good groups.
Example
Input
3
3 3 4 4 5
2 1 1 5 3
3 1 4 2 5
Output
2
2
0
Submitted Solution:
```
T = int(input())
#NumList=[3, 3, 4, 4, 5]
NumList=[2, 1, 1, 5, 3]
P = [input().split() for i in range(T)]
def ReturnGoodGroup(AXBYC):
NumList=AXBYC
A, X, B, Y, C = int(NumList[0]),int(NumList[1]),int(NumList[2]),int(NumList[3]),int(NumList[4])
RemainingBall=X+Y
GroupNum=0
BallList=[]
for A_times in range(X+1):
for B_times in range(Y+1):
if A_times+B_times>0 and (A*A_times+B*B_times)%C==0:
BallList.append([A_times,B_times])
OmomiBallList=[[x[0]/A,x[0]/B] for x in BallList]
#print(OmomiBallList)
BallNumSumList=[sum(x) for x in OmomiBallList]
OmomiSortedBallList = [x for _,x in sorted(zip(BallNumSumList,BallList))]
#print(OmomiSortedBallList)
A_Remain=X
B_Remain=Y
for ls in OmomiSortedBallList:
#print(ls)
A_Remain-=ls[0]
B_Remain-=ls[1]
# print("A_Remain:")
# print(A_Remain)
# print("B_Remain:")
# print(B_Remain)
if A_Remain>-1 and B_Remain>-1:
GroupNum+=1
elif A_Remain<0 or B_Remain<0:
break
return(GroupNum)
for AXBYC in P:
print(ReturnGoodGroup(AXBYC))
```
No
| 84,802 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has X+Y balls. X of them have an integer A written on them, and the other Y of them have an integer B written on them.
Snuke will divide these balls into some number of groups. Here, every ball should be contained in exactly one group, and every group should contain one or more balls.
A group is said to be good when the sum of the integers written on the balls in that group is a multiple of an integer C. Find the maximum possible number of good groups.
Solve T test cases for each input file.
Constraints
* 1 \leq T \leq 2 \times 10^4
* 1 \leq A,X,B,Y,C \leq 10^9
* A \neq B
Input
Input is given from Standard Input in the following format. The first line is as follows:
T
Then, T test cases follow. Each test case is given in the following format:
A X B Y C
Output
For each test case, print a line containing the maximum possible number of good groups.
Example
Input
3
3 3 4 4 5
2 1 1 5 3
3 1 4 2 5
Output
2
2
0
Submitted Solution:
```
import sys
from collections import deque
import itertools
def I(): return int(sys.stdin.readline().rstrip())
def LI():return list(map(int,sys.stdin.readline().rstrip().split()))
def LS():return list(sys.stdin.readline().rstrip().split())
def a(target, a, b, x, y):
# print("target=",target,"a=",a,"b=",b,"x=",x,"y=",y)
a_n = min(x, target // a)
b_n = min(y, target // b)
# print("a_n=",a_n, "target//a=",target//a, "b_n=",b_n,"target//b=",target//b)
comb = []
for a_i in range(a_n+1):
for b_i in range(b_n+1):
s = a * a_i + b * b_i
# print("target=",target,"a=",a_i,"b=",b_i,"s=",s)
if s == target:
comb.append((a_i,b_i))
return comb
def solver():
A,X,B,Y,C = LI()
# print("A=",A)
# print("X=",X)
# print("B=",B)
# print("Y=",Y)
# print("C=",C)
Total = A*X+B*Y
C_loop = Total//C
a_lmt = X
b_lmt = Y
ans = 0
for c_i in range(C_loop):
C_target = C * (c_i+1)
pattern = a(C_target, A, B, a_lmt, b_lmt)
print("target=",C_target, "pattern_num=",len(pattern))
ans += len(pattern)
for p in pattern:
# print("p=",p)
a_lmt -= p[0]
b_lmt -= p[1]
return ans
def main():
T = I()
# print("T=",T)
for _ in range(T):
# print("ANS=",solver())
print(solver())
if __name__ == '__main__':
main()
```
No
| 84,803 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has X+Y balls. X of them have an integer A written on them, and the other Y of them have an integer B written on them.
Snuke will divide these balls into some number of groups. Here, every ball should be contained in exactly one group, and every group should contain one or more balls.
A group is said to be good when the sum of the integers written on the balls in that group is a multiple of an integer C. Find the maximum possible number of good groups.
Solve T test cases for each input file.
Constraints
* 1 \leq T \leq 2 \times 10^4
* 1 \leq A,X,B,Y,C \leq 10^9
* A \neq B
Input
Input is given from Standard Input in the following format. The first line is as follows:
T
Then, T test cases follow. Each test case is given in the following format:
A X B Y C
Output
For each test case, print a line containing the maximum possible number of good groups.
Example
Input
3
3 3 4 4 5
2 1 1 5 3
3 1 4 2 5
Output
2
2
0
Submitted Solution:
```
import sys
from collections import deque
import itertools
def I(): return int(sys.stdin.readline().rstrip())
def LI():return list(map(int,sys.stdin.readline().rstrip().split()))
def LS():return list(sys.stdin.readline().rstrip().split())
def a(target, a, b, x, y):
# print("target=",target,"a=",a,"b=",b,"x=",x,"y=",y)
a_n = min(x, target // a)
b_n = min(y, target // b)
# print("a_n=",a_n, "target//a=",target//a, "b_n=",b_n,"target//b=",target//b)
comb = []
for a_i in range(a_n+1):
for b_i in range(b_n+1):
s = a * a_i + b * b_i
# print("target=",target,"a=",a_i,"b=",b_i,"s=",s)
if s == target:
comb.append((a_i,b_i))
return comb
def solver():
A,X,B,Y,C = LI()
# print("A=",A)
# print("X=",X)
# print("B=",B)
# print("Y=",Y)
# print("C=",C)
Total = A*X+B*Y
C_loop = Total//C
a_lmt = X
b_lmt = Y
ans = 0
for c_i in range(C_loop):
C_target = C * (c_i+1)
pattern = a(C_target, A, B, a_lmt, b_lmt)
# print("target=",C_target, "pattern_num=",len(pattern))
ans += len(pattern)
for p in pattern:
# print("p=",p)
a_lmt -= p[0]
b_lmt -= p[1]
return ans
def main():
T = I()
# print("T=",T)
for _ in range(T):
# print("ANS=",solver())
print(solver())
if __name__ == '__main__':
main()
```
No
| 84,804 |
Provide a correct Python 3 solution for this coding contest problem.
Fennec is fighting with N monsters.
The health of the i-th monster is H_i.
Fennec can do the following two actions:
* Attack: Fennec chooses one monster. That monster's health will decrease by 1.
* Special Move: Fennec chooses one monster. That monster's health will become 0.
There is no way other than Attack and Special Move to decrease the monsters' health.
Fennec wins when all the monsters' healths become 0 or below.
Find the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning when she can use Special Move at most K times.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq K \leq 2 \times 10^5
* 1 \leq H_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
H_1 ... H_N
Output
Print the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning.
Examples
Input
3 1
4 1 5
Output
5
Input
8 9
7 9 3 2 3 8 4 6
Output
0
Input
3 0
1000000000 1000000000 1000000000
Output
3000000000
"Correct Solution:
```
n,k,*h=map(int,open(0).read().split())
if k>=n:
print(0)
exit()
h.sort()
print(sum(h[:n-k]))
```
| 84,805 |
Provide a correct Python 3 solution for this coding contest problem.
Fennec is fighting with N monsters.
The health of the i-th monster is H_i.
Fennec can do the following two actions:
* Attack: Fennec chooses one monster. That monster's health will decrease by 1.
* Special Move: Fennec chooses one monster. That monster's health will become 0.
There is no way other than Attack and Special Move to decrease the monsters' health.
Fennec wins when all the monsters' healths become 0 or below.
Find the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning when she can use Special Move at most K times.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq K \leq 2 \times 10^5
* 1 \leq H_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
H_1 ... H_N
Output
Print the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning.
Examples
Input
3 1
4 1 5
Output
5
Input
8 9
7 9 3 2 3 8 4 6
Output
0
Input
3 0
1000000000 1000000000 1000000000
Output
3000000000
"Correct Solution:
```
R = lambda: map(int, input().split())
n, k = R()
print(sum(sorted(R())[:n - k]) if k < n else 0)
```
| 84,806 |
Provide a correct Python 3 solution for this coding contest problem.
Fennec is fighting with N monsters.
The health of the i-th monster is H_i.
Fennec can do the following two actions:
* Attack: Fennec chooses one monster. That monster's health will decrease by 1.
* Special Move: Fennec chooses one monster. That monster's health will become 0.
There is no way other than Attack and Special Move to decrease the monsters' health.
Fennec wins when all the monsters' healths become 0 or below.
Find the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning when she can use Special Move at most K times.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq K \leq 2 \times 10^5
* 1 \leq H_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
H_1 ... H_N
Output
Print the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning.
Examples
Input
3 1
4 1 5
Output
5
Input
8 9
7 9 3 2 3 8 4 6
Output
0
Input
3 0
1000000000 1000000000 1000000000
Output
3000000000
"Correct Solution:
```
N,H=map(int,input().split())
Mon=list(map(int,input().split()))
Mon=sorted(Mon)[::-1]
print(sum(Mon[H::]))
```
| 84,807 |
Provide a correct Python 3 solution for this coding contest problem.
Fennec is fighting with N monsters.
The health of the i-th monster is H_i.
Fennec can do the following two actions:
* Attack: Fennec chooses one monster. That monster's health will decrease by 1.
* Special Move: Fennec chooses one monster. That monster's health will become 0.
There is no way other than Attack and Special Move to decrease the monsters' health.
Fennec wins when all the monsters' healths become 0 or below.
Find the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning when she can use Special Move at most K times.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq K \leq 2 \times 10^5
* 1 \leq H_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
H_1 ... H_N
Output
Print the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning.
Examples
Input
3 1
4 1 5
Output
5
Input
8 9
7 9 3 2 3 8 4 6
Output
0
Input
3 0
1000000000 1000000000 1000000000
Output
3000000000
"Correct Solution:
```
N, K = map(int, input().split())
*H, = sorted(map(int, input().split()), reverse=True)
print(sum(H[K:]))
```
| 84,808 |
Provide a correct Python 3 solution for this coding contest problem.
Fennec is fighting with N monsters.
The health of the i-th monster is H_i.
Fennec can do the following two actions:
* Attack: Fennec chooses one monster. That monster's health will decrease by 1.
* Special Move: Fennec chooses one monster. That monster's health will become 0.
There is no way other than Attack and Special Move to decrease the monsters' health.
Fennec wins when all the monsters' healths become 0 or below.
Find the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning when she can use Special Move at most K times.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq K \leq 2 \times 10^5
* 1 \leq H_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
H_1 ... H_N
Output
Print the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning.
Examples
Input
3 1
4 1 5
Output
5
Input
8 9
7 9 3 2 3 8 4 6
Output
0
Input
3 0
1000000000 1000000000 1000000000
Output
3000000000
"Correct Solution:
```
N,K = map(int,input().split())
print(sum(sorted(map(int,input().split()))[:max(0,N-K)]))
```
| 84,809 |
Provide a correct Python 3 solution for this coding contest problem.
Fennec is fighting with N monsters.
The health of the i-th monster is H_i.
Fennec can do the following two actions:
* Attack: Fennec chooses one monster. That monster's health will decrease by 1.
* Special Move: Fennec chooses one monster. That monster's health will become 0.
There is no way other than Attack and Special Move to decrease the monsters' health.
Fennec wins when all the monsters' healths become 0 or below.
Find the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning when she can use Special Move at most K times.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq K \leq 2 \times 10^5
* 1 \leq H_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
H_1 ... H_N
Output
Print the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning.
Examples
Input
3 1
4 1 5
Output
5
Input
8 9
7 9 3 2 3 8 4 6
Output
0
Input
3 0
1000000000 1000000000 1000000000
Output
3000000000
"Correct Solution:
```
N,K = map(int,input().split())
H = sorted(list(map(int,input().split())))[::-1]
print(sum(H[K:]))
```
| 84,810 |
Provide a correct Python 3 solution for this coding contest problem.
Fennec is fighting with N monsters.
The health of the i-th monster is H_i.
Fennec can do the following two actions:
* Attack: Fennec chooses one monster. That monster's health will decrease by 1.
* Special Move: Fennec chooses one monster. That monster's health will become 0.
There is no way other than Attack and Special Move to decrease the monsters' health.
Fennec wins when all the monsters' healths become 0 or below.
Find the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning when she can use Special Move at most K times.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq K \leq 2 \times 10^5
* 1 \leq H_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
H_1 ... H_N
Output
Print the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning.
Examples
Input
3 1
4 1 5
Output
5
Input
8 9
7 9 3 2 3 8 4 6
Output
0
Input
3 0
1000000000 1000000000 1000000000
Output
3000000000
"Correct Solution:
```
N,K = map(int,input().split())
H = list(map(int,input().split()))
H.sort(reverse=True)
print(sum(H[K::]))
```
| 84,811 |
Provide a correct Python 3 solution for this coding contest problem.
Fennec is fighting with N monsters.
The health of the i-th monster is H_i.
Fennec can do the following two actions:
* Attack: Fennec chooses one monster. That monster's health will decrease by 1.
* Special Move: Fennec chooses one monster. That monster's health will become 0.
There is no way other than Attack and Special Move to decrease the monsters' health.
Fennec wins when all the monsters' healths become 0 or below.
Find the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning when she can use Special Move at most K times.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq K \leq 2 \times 10^5
* 1 \leq H_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
H_1 ... H_N
Output
Print the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning.
Examples
Input
3 1
4 1 5
Output
5
Input
8 9
7 9 3 2 3 8 4 6
Output
0
Input
3 0
1000000000 1000000000 1000000000
Output
3000000000
"Correct Solution:
```
n,k = map(int,input().split())
l=sorted(list(map(int,input().split())))
print(sum(l[:max(0,n-k)]))
```
| 84,812 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Fennec is fighting with N monsters.
The health of the i-th monster is H_i.
Fennec can do the following two actions:
* Attack: Fennec chooses one monster. That monster's health will decrease by 1.
* Special Move: Fennec chooses one monster. That monster's health will become 0.
There is no way other than Attack and Special Move to decrease the monsters' health.
Fennec wins when all the monsters' healths become 0 or below.
Find the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning when she can use Special Move at most K times.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq K \leq 2 \times 10^5
* 1 \leq H_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
H_1 ... H_N
Output
Print the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning.
Examples
Input
3 1
4 1 5
Output
5
Input
8 9
7 9 3 2 3 8 4 6
Output
0
Input
3 0
1000000000 1000000000 1000000000
Output
3000000000
Submitted Solution:
```
n,k = map(int,input().split())
a = list(map(int,input().split()))
a.sort(reverse=1)
print(sum(a[k:]))
```
Yes
| 84,813 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Fennec is fighting with N monsters.
The health of the i-th monster is H_i.
Fennec can do the following two actions:
* Attack: Fennec chooses one monster. That monster's health will decrease by 1.
* Special Move: Fennec chooses one monster. That monster's health will become 0.
There is no way other than Attack and Special Move to decrease the monsters' health.
Fennec wins when all the monsters' healths become 0 or below.
Find the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning when she can use Special Move at most K times.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq K \leq 2 \times 10^5
* 1 \leq H_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
H_1 ... H_N
Output
Print the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning.
Examples
Input
3 1
4 1 5
Output
5
Input
8 9
7 9 3 2 3 8 4 6
Output
0
Input
3 0
1000000000 1000000000 1000000000
Output
3000000000
Submitted Solution:
```
N,K=map(int,input().split())
H=list(map(int,input().split()))
H=sorted(H)[::-1]
print(sum(H[K:]))
```
Yes
| 84,814 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Fennec is fighting with N monsters.
The health of the i-th monster is H_i.
Fennec can do the following two actions:
* Attack: Fennec chooses one monster. That monster's health will decrease by 1.
* Special Move: Fennec chooses one monster. That monster's health will become 0.
There is no way other than Attack and Special Move to decrease the monsters' health.
Fennec wins when all the monsters' healths become 0 or below.
Find the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning when she can use Special Move at most K times.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq K \leq 2 \times 10^5
* 1 \leq H_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
H_1 ... H_N
Output
Print the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning.
Examples
Input
3 1
4 1 5
Output
5
Input
8 9
7 9 3 2 3 8 4 6
Output
0
Input
3 0
1000000000 1000000000 1000000000
Output
3000000000
Submitted Solution:
```
n,k,*h=map(int,open(0).read().split())
if n<k:
print(0)
else:
h.sort()
h=h[:(n-k)]
print(sum(h))
```
Yes
| 84,815 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Fennec is fighting with N monsters.
The health of the i-th monster is H_i.
Fennec can do the following two actions:
* Attack: Fennec chooses one monster. That monster's health will decrease by 1.
* Special Move: Fennec chooses one monster. That monster's health will become 0.
There is no way other than Attack and Special Move to decrease the monsters' health.
Fennec wins when all the monsters' healths become 0 or below.
Find the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning when she can use Special Move at most K times.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq K \leq 2 \times 10^5
* 1 \leq H_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
H_1 ... H_N
Output
Print the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning.
Examples
Input
3 1
4 1 5
Output
5
Input
8 9
7 9 3 2 3 8 4 6
Output
0
Input
3 0
1000000000 1000000000 1000000000
Output
3000000000
Submitted Solution:
```
n,k=map(int,input().split())
l=list(map(int,input().split()))
l.sort(reverse=True)
s=sum(l[k:])
print(s)
```
Yes
| 84,816 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Fennec is fighting with N monsters.
The health of the i-th monster is H_i.
Fennec can do the following two actions:
* Attack: Fennec chooses one monster. That monster's health will decrease by 1.
* Special Move: Fennec chooses one monster. That monster's health will become 0.
There is no way other than Attack and Special Move to decrease the monsters' health.
Fennec wins when all the monsters' healths become 0 or below.
Find the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning when she can use Special Move at most K times.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq K \leq 2 \times 10^5
* 1 \leq H_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
H_1 ... H_N
Output
Print the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning.
Examples
Input
3 1
4 1 5
Output
5
Input
8 9
7 9 3 2 3 8 4 6
Output
0
Input
3 0
1000000000 1000000000 1000000000
Output
3000000000
Submitted Solution:
```
arr = input().split(" ")
N = int(arr[0])
K = int(arr[1])
HP_arr = input().split(" ")
HP_arr.sort(reverse=True)
HP_arr = [int(i) for i in HP_arr ]
while(True):
if(K > 0):
HP_arr.pop(0)
K -= 1
else:
break
print(sum(HP_arr))
```
No
| 84,817 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Fennec is fighting with N monsters.
The health of the i-th monster is H_i.
Fennec can do the following two actions:
* Attack: Fennec chooses one monster. That monster's health will decrease by 1.
* Special Move: Fennec chooses one monster. That monster's health will become 0.
There is no way other than Attack and Special Move to decrease the monsters' health.
Fennec wins when all the monsters' healths become 0 or below.
Find the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning when she can use Special Move at most K times.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq K \leq 2 \times 10^5
* 1 \leq H_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
H_1 ... H_N
Output
Print the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning.
Examples
Input
3 1
4 1 5
Output
5
Input
8 9
7 9 3 2 3 8 4 6
Output
0
Input
3 0
1000000000 1000000000 1000000000
Output
3000000000
Submitted Solution:
```
n, k = map(int, input().split())
if n <= k:
print(0)
elif k == 0:
print(sum(h))
else:
h = sorted(list(map(int, input().split())))
print(sum(h[:n-k]))
```
No
| 84,818 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Fennec is fighting with N monsters.
The health of the i-th monster is H_i.
Fennec can do the following two actions:
* Attack: Fennec chooses one monster. That monster's health will decrease by 1.
* Special Move: Fennec chooses one monster. That monster's health will become 0.
There is no way other than Attack and Special Move to decrease the monsters' health.
Fennec wins when all the monsters' healths become 0 or below.
Find the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning when she can use Special Move at most K times.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq K \leq 2 \times 10^5
* 1 \leq H_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
H_1 ... H_N
Output
Print the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning.
Examples
Input
3 1
4 1 5
Output
5
Input
8 9
7 9 3 2 3 8 4 6
Output
0
Input
3 0
1000000000 1000000000 1000000000
Output
3000000000
Submitted Solution:
```
N, K = map(int, input().split())
H = [int(N) for N in input().split()]
for i in range(0, K):
max_index = H.index(max(H))
H[max_index] = 0
print(sum(int(i) for i in H))
```
No
| 84,819 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Fennec is fighting with N monsters.
The health of the i-th monster is H_i.
Fennec can do the following two actions:
* Attack: Fennec chooses one monster. That monster's health will decrease by 1.
* Special Move: Fennec chooses one monster. That monster's health will become 0.
There is no way other than Attack and Special Move to decrease the monsters' health.
Fennec wins when all the monsters' healths become 0 or below.
Find the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning when she can use Special Move at most K times.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq K \leq 2 \times 10^5
* 1 \leq H_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
H_1 ... H_N
Output
Print the minimum number of times Fennec needs to do Attack (not counting Special Move) before winning.
Examples
Input
3 1
4 1 5
Output
5
Input
8 9
7 9 3 2 3 8 4 6
Output
0
Input
3 0
1000000000 1000000000 1000000000
Output
3000000000
Submitted Solution:
```
#C
NK = input().split(' ')
N = int(NK[0])
K = int(NK[1])
Hi = input().split(' ')
Hi.sort()
for s in range(K):
Hi.pop(N - 1 - s)
count = 0
for j in range(N-K):
count += int(Hi[j])
print(count)
```
No
| 84,820 |
Provide a correct Python 3 solution for this coding contest problem.
You will be given a string S of length 3 representing the weather forecast for three days in the past.
The i-th character (1 \leq i \leq 3) of S represents the forecast for the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
You will also be given a string T of length 3 representing the actual weather on those three days.
The i-th character (1 \leq i \leq 3) of S represents the actual weather on the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
Print the number of days for which the forecast was correct.
Constraints
* S and T are strings of length 3 each.
* S and T consist of `S`, `C`, and `R`.
Input
Input is given from Standard Input in the following format:
S
T
Output
Print the number of days for which the forecast was correct.
Examples
Input
CSS
CSR
Output
2
Input
SSR
SSR
Output
3
Input
RRR
SSS
Output
0
"Correct Solution:
```
s=input()
t=input()
print(int(s[0]==t[0])+int(s[2]==t[2])+int(s[1]==t[1]))
```
| 84,821 |
Provide a correct Python 3 solution for this coding contest problem.
You will be given a string S of length 3 representing the weather forecast for three days in the past.
The i-th character (1 \leq i \leq 3) of S represents the forecast for the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
You will also be given a string T of length 3 representing the actual weather on those three days.
The i-th character (1 \leq i \leq 3) of S represents the actual weather on the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
Print the number of days for which the forecast was correct.
Constraints
* S and T are strings of length 3 each.
* S and T consist of `S`, `C`, and `R`.
Input
Input is given from Standard Input in the following format:
S
T
Output
Print the number of days for which the forecast was correct.
Examples
Input
CSS
CSR
Output
2
Input
SSR
SSR
Output
3
Input
RRR
SSS
Output
0
"Correct Solution:
```
S = input().rstrip()
T = input().rstrip()
print(sum(s == t for s, t in zip(S, T)))
```
| 84,822 |
Provide a correct Python 3 solution for this coding contest problem.
You will be given a string S of length 3 representing the weather forecast for three days in the past.
The i-th character (1 \leq i \leq 3) of S represents the forecast for the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
You will also be given a string T of length 3 representing the actual weather on those three days.
The i-th character (1 \leq i \leq 3) of S represents the actual weather on the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
Print the number of days for which the forecast was correct.
Constraints
* S and T are strings of length 3 each.
* S and T consist of `S`, `C`, and `R`.
Input
Input is given from Standard Input in the following format:
S
T
Output
Print the number of days for which the forecast was correct.
Examples
Input
CSS
CSR
Output
2
Input
SSR
SSR
Output
3
Input
RRR
SSS
Output
0
"Correct Solution:
```
s = input()
t = input()
ans = len([1 for si,ti in zip(s,t) if si == ti])
print(ans)
```
| 84,823 |
Provide a correct Python 3 solution for this coding contest problem.
You will be given a string S of length 3 representing the weather forecast for three days in the past.
The i-th character (1 \leq i \leq 3) of S represents the forecast for the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
You will also be given a string T of length 3 representing the actual weather on those three days.
The i-th character (1 \leq i \leq 3) of S represents the actual weather on the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
Print the number of days for which the forecast was correct.
Constraints
* S and T are strings of length 3 each.
* S and T consist of `S`, `C`, and `R`.
Input
Input is given from Standard Input in the following format:
S
T
Output
Print the number of days for which the forecast was correct.
Examples
Input
CSS
CSR
Output
2
Input
SSR
SSR
Output
3
Input
RRR
SSS
Output
0
"Correct Solution:
```
ss = input()
tt = input()
print(sum([s==t for s, t in zip(ss,tt)]))
```
| 84,824 |
Provide a correct Python 3 solution for this coding contest problem.
You will be given a string S of length 3 representing the weather forecast for three days in the past.
The i-th character (1 \leq i \leq 3) of S represents the forecast for the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
You will also be given a string T of length 3 representing the actual weather on those three days.
The i-th character (1 \leq i \leq 3) of S represents the actual weather on the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
Print the number of days for which the forecast was correct.
Constraints
* S and T are strings of length 3 each.
* S and T consist of `S`, `C`, and `R`.
Input
Input is given from Standard Input in the following format:
S
T
Output
Print the number of days for which the forecast was correct.
Examples
Input
CSS
CSR
Output
2
Input
SSR
SSR
Output
3
Input
RRR
SSS
Output
0
"Correct Solution:
```
S=input()
T=input()
c=0
for s,t in zip(S,T):
if s==t:
c+=1
print(c)
```
| 84,825 |
Provide a correct Python 3 solution for this coding contest problem.
You will be given a string S of length 3 representing the weather forecast for three days in the past.
The i-th character (1 \leq i \leq 3) of S represents the forecast for the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
You will also be given a string T of length 3 representing the actual weather on those three days.
The i-th character (1 \leq i \leq 3) of S represents the actual weather on the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
Print the number of days for which the forecast was correct.
Constraints
* S and T are strings of length 3 each.
* S and T consist of `S`, `C`, and `R`.
Input
Input is given from Standard Input in the following format:
S
T
Output
Print the number of days for which the forecast was correct.
Examples
Input
CSS
CSR
Output
2
Input
SSR
SSR
Output
3
Input
RRR
SSS
Output
0
"Correct Solution:
```
s1=input()
s2=input()
print(sum(s1[i]==s2[i] for i in range(len(s1))))
```
| 84,826 |
Provide a correct Python 3 solution for this coding contest problem.
You will be given a string S of length 3 representing the weather forecast for three days in the past.
The i-th character (1 \leq i \leq 3) of S represents the forecast for the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
You will also be given a string T of length 3 representing the actual weather on those three days.
The i-th character (1 \leq i \leq 3) of S represents the actual weather on the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
Print the number of days for which the forecast was correct.
Constraints
* S and T are strings of length 3 each.
* S and T consist of `S`, `C`, and `R`.
Input
Input is given from Standard Input in the following format:
S
T
Output
Print the number of days for which the forecast was correct.
Examples
Input
CSS
CSR
Output
2
Input
SSR
SSR
Output
3
Input
RRR
SSS
Output
0
"Correct Solution:
```
print(3-sum(i!=j for i,j in zip(*open(0))))
```
| 84,827 |
Provide a correct Python 3 solution for this coding contest problem.
You will be given a string S of length 3 representing the weather forecast for three days in the past.
The i-th character (1 \leq i \leq 3) of S represents the forecast for the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
You will also be given a string T of length 3 representing the actual weather on those three days.
The i-th character (1 \leq i \leq 3) of S represents the actual weather on the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
Print the number of days for which the forecast was correct.
Constraints
* S and T are strings of length 3 each.
* S and T consist of `S`, `C`, and `R`.
Input
Input is given from Standard Input in the following format:
S
T
Output
Print the number of days for which the forecast was correct.
Examples
Input
CSS
CSR
Output
2
Input
SSR
SSR
Output
3
Input
RRR
SSS
Output
0
"Correct Solution:
```
s=input()
t=input()
print(sum([s[i]==t[i] for i in range(3)]))
```
| 84,828 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You will be given a string S of length 3 representing the weather forecast for three days in the past.
The i-th character (1 \leq i \leq 3) of S represents the forecast for the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
You will also be given a string T of length 3 representing the actual weather on those three days.
The i-th character (1 \leq i \leq 3) of S represents the actual weather on the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
Print the number of days for which the forecast was correct.
Constraints
* S and T are strings of length 3 each.
* S and T consist of `S`, `C`, and `R`.
Input
Input is given from Standard Input in the following format:
S
T
Output
Print the number of days for which the forecast was correct.
Examples
Input
CSS
CSR
Output
2
Input
SSR
SSR
Output
3
Input
RRR
SSS
Output
0
Submitted Solution:
```
s = input()
t = input()
print(len([v for i,v in enumerate(s) if (t[i] == v)]))
```
Yes
| 84,829 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You will be given a string S of length 3 representing the weather forecast for three days in the past.
The i-th character (1 \leq i \leq 3) of S represents the forecast for the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
You will also be given a string T of length 3 representing the actual weather on those three days.
The i-th character (1 \leq i \leq 3) of S represents the actual weather on the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
Print the number of days for which the forecast was correct.
Constraints
* S and T are strings of length 3 each.
* S and T consist of `S`, `C`, and `R`.
Input
Input is given from Standard Input in the following format:
S
T
Output
Print the number of days for which the forecast was correct.
Examples
Input
CSS
CSR
Output
2
Input
SSR
SSR
Output
3
Input
RRR
SSS
Output
0
Submitted Solution:
```
a,b = input(),input()
c = 0
for i in[0,1,2]:
c = c + int(a[i] == b[i])
print(c)
```
Yes
| 84,830 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You will be given a string S of length 3 representing the weather forecast for three days in the past.
The i-th character (1 \leq i \leq 3) of S represents the forecast for the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
You will also be given a string T of length 3 representing the actual weather on those three days.
The i-th character (1 \leq i \leq 3) of S represents the actual weather on the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
Print the number of days for which the forecast was correct.
Constraints
* S and T are strings of length 3 each.
* S and T consist of `S`, `C`, and `R`.
Input
Input is given from Standard Input in the following format:
S
T
Output
Print the number of days for which the forecast was correct.
Examples
Input
CSS
CSR
Output
2
Input
SSR
SSR
Output
3
Input
RRR
SSS
Output
0
Submitted Solution:
```
print(sum(x==y for x,y in zip(input(),input())))
```
Yes
| 84,831 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You will be given a string S of length 3 representing the weather forecast for three days in the past.
The i-th character (1 \leq i \leq 3) of S represents the forecast for the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
You will also be given a string T of length 3 representing the actual weather on those three days.
The i-th character (1 \leq i \leq 3) of S represents the actual weather on the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
Print the number of days for which the forecast was correct.
Constraints
* S and T are strings of length 3 each.
* S and T consist of `S`, `C`, and `R`.
Input
Input is given from Standard Input in the following format:
S
T
Output
Print the number of days for which the forecast was correct.
Examples
Input
CSS
CSR
Output
2
Input
SSR
SSR
Output
3
Input
RRR
SSS
Output
0
Submitted Solution:
```
s = input()
t = input()
a=0
a+=(s[0]==t[0])+(s[1]==t[1])+(s[2]==t[2])
print(a)
```
Yes
| 84,832 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You will be given a string S of length 3 representing the weather forecast for three days in the past.
The i-th character (1 \leq i \leq 3) of S represents the forecast for the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
You will also be given a string T of length 3 representing the actual weather on those three days.
The i-th character (1 \leq i \leq 3) of S represents the actual weather on the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
Print the number of days for which the forecast was correct.
Constraints
* S and T are strings of length 3 each.
* S and T consist of `S`, `C`, and `R`.
Input
Input is given from Standard Input in the following format:
S
T
Output
Print the number of days for which the forecast was correct.
Examples
Input
CSS
CSR
Output
2
Input
SSR
SSR
Output
3
Input
RRR
SSS
Output
0
Submitted Solution:
```
#Tenki
S = input()
T = input()
ctr = 0
for i in range(len(S)):
if S[i] == T[i]:
ctr = ctr+1
```
No
| 84,833 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You will be given a string S of length 3 representing the weather forecast for three days in the past.
The i-th character (1 \leq i \leq 3) of S represents the forecast for the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
You will also be given a string T of length 3 representing the actual weather on those three days.
The i-th character (1 \leq i \leq 3) of S represents the actual weather on the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
Print the number of days for which the forecast was correct.
Constraints
* S and T are strings of length 3 each.
* S and T consist of `S`, `C`, and `R`.
Input
Input is given from Standard Input in the following format:
S
T
Output
Print the number of days for which the forecast was correct.
Examples
Input
CSS
CSR
Output
2
Input
SSR
SSR
Output
3
Input
RRR
SSS
Output
0
Submitted Solution:
```
s = input()
t = input()
x = 0
for i in 3:
x += s[i-1]!=t[i-1]
print(x)
```
No
| 84,834 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You will be given a string S of length 3 representing the weather forecast for three days in the past.
The i-th character (1 \leq i \leq 3) of S represents the forecast for the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
You will also be given a string T of length 3 representing the actual weather on those three days.
The i-th character (1 \leq i \leq 3) of S represents the actual weather on the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
Print the number of days for which the forecast was correct.
Constraints
* S and T are strings of length 3 each.
* S and T consist of `S`, `C`, and `R`.
Input
Input is given from Standard Input in the following format:
S
T
Output
Print the number of days for which the forecast was correct.
Examples
Input
CSS
CSR
Output
2
Input
SSR
SSR
Output
3
Input
RRR
SSS
Output
0
Submitted Solution:
```
N = int(input())
A=[int(_) for _ in input().split()]
Maxcounter = 0
for i in range(1,N):
counter = 0
k = i
while k < N:
if (A[k-1]>=A[k]):
counter += 1
k += 1
if Maxcounter <= counter:
Maxcounter = counter
else:
break
print(Maxcounter)
```
No
| 84,835 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You will be given a string S of length 3 representing the weather forecast for three days in the past.
The i-th character (1 \leq i \leq 3) of S represents the forecast for the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
You will also be given a string T of length 3 representing the actual weather on those three days.
The i-th character (1 \leq i \leq 3) of S represents the actual weather on the i-th day. `S`, `C`, and `R` stand for sunny, cloudy, and rainy, respectively.
Print the number of days for which the forecast was correct.
Constraints
* S and T are strings of length 3 each.
* S and T consist of `S`, `C`, and `R`.
Input
Input is given from Standard Input in the following format:
S
T
Output
Print the number of days for which the forecast was correct.
Examples
Input
CSS
CSR
Output
2
Input
SSR
SSR
Output
3
Input
RRR
SSS
Output
0
Submitted Solution:
```
n = int(input())
h = list(map(int,input().split()))
ans = 0
ls = []
for i in range(n-1):
if h[i] >= h[i+1]:
ans += 1
else:
ls.append(ans)
ans = 0
ls.append(ans)
print(max(ls))
```
No
| 84,836 |
Provide a correct Python 3 solution for this coding contest problem.
Note the unusual memory limit.
For a rectangular grid where each square is painted white or black, we define its complexity as follows:
* If all the squares are black or all the squares are white, the complexity is 0.
* Otherwise, divide the grid into two subgrids by a line parallel to one of the sides of the grid, and let c_1 and c_2 be the complexities of the subgrids. There can be multiple ways to perform the division, and let m be the minimum value of \max(c_1, c_2) in those divisions. The complexity of the grid is m+1.
You are given a grid with H horizontal rows and W vertical columns where each square is painted white or black. HW characters from A_{11} to A_{HW} represent the colors of the squares. A_{ij} is `#` if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is `.` if that square is white.
Find the complexity of the given grid.
Constraints
* 1 \leq H,W \leq 185
* A_{ij} is `#` or `.`.
Input
Input is given from Standard Input in the following format:
H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}
Output
Print the complexity of the given grid.
Examples
Input
3 3
...
.##
.##
Output
2
Input
6 7
.####.#
....#.
....#.
....#.
.####.#
....##
Output
4
"Correct Solution:
```
H, W = map(int, input().split())
A = [[1 if a == "#" else 0 for a in input()] for _ in range(H)]
X = [[[-2] * (H + 2) for _ in range(W + 2)] for _ in range(H + 2)]
Y = [[[-2] * (W + 2) for _ in range(W + 2)] for _ in range(H + 2)]
for i in range(H):
for j in range(W):
X[i][j][i] = j
Y[i][j][j] = i
for i in range(H):
for j in range(W-1)[::-1]:
if A[i][j] == A[i][j+1]:
X[i][j][i] = X[i][j+1][i]
for i in range(H-1)[::-1]:
for j in range(W):
if A[i][j] == A[i+1][j]:
Y[i][j][j] = Y[i+1][j][j]
for i in range(H):
for j in range(W):
for ii in range(i+1, H):
if A[ii][j] != A[i][j]:
break
X[i][j][ii] = min(X[i][j][ii-1], X[ii][j][ii])
for i in range(H):
for j in range(W):
for jj in range(j+1, W):
if A[i][jj] != A[i][j]:
break
Y[i][j][jj] = min(Y[i][j][jj-1], Y[i][jj][jj])
for k in range(16):
if X[0][0][H-1] == W-1:
print(k)
break
elif k == 15:
print(16)
break
for i in range(H):
Xi = X[i]
Yi = Y[i]
for j in range(W):
Xij = Xi[j]
Yij = Yi[j]
for ii in range(i, H):
Xijii = Xij[ii]
if Xijii >= 0 and X[i][Xijii + 1][ii] >= 0:
Xij[ii] = X[i][Xijii + 1][ii]
for jj in range(j, W):
Yijjj = Yij[jj]
if Yijjj >= 0 and Y[Yijjj + 1][j][jj] >= 0:
Yij[jj] = Y[Yijjj + 1][j][jj]
jj = W - 1
for ii in range(i, H):
while jj >= j and Yij[jj] < ii:
jj -= 1
if jj >= j:
Xij[ii] = max(Xij[ii], jj)
ii = H - 1
for jj in range(j, W):
while ii >= i and Xij[ii] < jj:
ii -= 1
if ii >= i:
Yij[jj] = max(Yij[jj], ii)
```
| 84,837 |
Provide a correct Python 3 solution for this coding contest problem.
Note the unusual memory limit.
For a rectangular grid where each square is painted white or black, we define its complexity as follows:
* If all the squares are black or all the squares are white, the complexity is 0.
* Otherwise, divide the grid into two subgrids by a line parallel to one of the sides of the grid, and let c_1 and c_2 be the complexities of the subgrids. There can be multiple ways to perform the division, and let m be the minimum value of \max(c_1, c_2) in those divisions. The complexity of the grid is m+1.
You are given a grid with H horizontal rows and W vertical columns where each square is painted white or black. HW characters from A_{11} to A_{HW} represent the colors of the squares. A_{ij} is `#` if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is `.` if that square is white.
Find the complexity of the given grid.
Constraints
* 1 \leq H,W \leq 185
* A_{ij} is `#` or `.`.
Input
Input is given from Standard Input in the following format:
H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}
Output
Print the complexity of the given grid.
Examples
Input
3 3
...
.##
.##
Output
2
Input
6 7
.####.#
....#.
....#.
....#.
.####.#
....##
Output
4
"Correct Solution:
```
h, w = map(int, input().split())
field = [input() for _ in [0] * h]
HR = list(range(h))
WR = list(range(w))
WR2 = list(range(w - 2, -1, -1))
# horizontal dp, vertical dp
hor = [[[-1] * h for _ in WR] for _ in HR] # hor[top][left][bottom] = right
ver = [[[-1] * w for _ in WR] for _ in HR] # ver[top][left][right] = bottom
for i in HR:
hi = hor[i]
fi = field[i]
curr = hi[-1][i] = w - 1
curc = fi[-1]
for j in WR2:
if fi[j] != curc:
curr = hi[j][i] = j
curc = fi[j]
else:
hi[j][i] = curr
for i in HR:
hi = hor[i]
vi = ver[i]
fi = field[i]
for j in WR:
hij = hi[j]
vij = vi[j]
fij = fi[j]
curr = hij[i]
for k in HR[i + 1:]:
if field[k][j] != fij:
break
curr = hij[k] = min(curr, hor[k][j][k])
curr = j
for k in range(h - 1, i - 1, -1):
h_ijk = hij[k]
if h_ijk == -1:
continue
while curr <= h_ijk:
vij[curr] = k
curr += 1
ans = 0
while True:
if hor[0][0][-1] == w - 1:
break
for i in HR:
hi = hor[i]
vi = ver[i]
for j in WR:
hij = hi[j]
vij = vi[j]
# print(ans + 1, i, j, 'first')
# print(hor[i][j])
# print(ver[i][j])
# Update hor using hor, ver using ver
for k in HR[i:]:
h_ijk = hij[k]
if h_ijk == -1:
break
if h_ijk == w - 1:
continue
hij[k] = max(h_ijk, hi[h_ijk + 1][k])
for k in WR[j:]:
v_ijk = vij[k]
if v_ijk == -1:
break
if v_ijk == h - 1:
continue
vij[k] = max(v_ijk, ver[v_ijk + 1][j][k])
# print(ans + 1, i, j, 'before')
# print(hor[i][j])
# print(ver[i][j])
# Update hor using ver, ver using hor
curr = j
for k in range(h - 1, i - 1, -1):
h_ijk = hij[k]
if h_ijk == -1:
continue
while curr <= h_ijk:
vij[curr] = max(vij[curr], k)
curr += 1
curb = i
for k in range(w - 1, j - 1, -1):
v_ijk = vij[k]
if v_ijk == -1:
continue
while curb <= v_ijk:
hij[curb] = max(hij[curb], k)
curb += 1
# print(ans + 1, i, j, 'after')
# print(hor[i][j])
# print(ver[i][j])
ans += 1
print(ans)
```
| 84,838 |
Provide a correct Python 3 solution for this coding contest problem.
Note the unusual memory limit.
For a rectangular grid where each square is painted white or black, we define its complexity as follows:
* If all the squares are black or all the squares are white, the complexity is 0.
* Otherwise, divide the grid into two subgrids by a line parallel to one of the sides of the grid, and let c_1 and c_2 be the complexities of the subgrids. There can be multiple ways to perform the division, and let m be the minimum value of \max(c_1, c_2) in those divisions. The complexity of the grid is m+1.
You are given a grid with H horizontal rows and W vertical columns where each square is painted white or black. HW characters from A_{11} to A_{HW} represent the colors of the squares. A_{ij} is `#` if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is `.` if that square is white.
Find the complexity of the given grid.
Constraints
* 1 \leq H,W \leq 185
* A_{ij} is `#` or `.`.
Input
Input is given from Standard Input in the following format:
H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}
Output
Print the complexity of the given grid.
Examples
Input
3 3
...
.##
.##
Output
2
Input
6 7
.####.#
....#.
....#.
....#.
.####.#
....##
Output
4
"Correct Solution:
```
h, w = map(int, input().split())
field = [input() for _ in [0] * h]
HR = list(range(h))
WR = list(range(w))
WR2 = list(range(w - 2, -1, -1))
# horizontal dp, vertical dp
hor = [[[-1] * h for _ in WR] for _ in HR] # hor[top][left][bottom] = right
ver = [[[-1] * w for _ in WR] for _ in HR] # ver[top][left][right] = bottom
for i in HR:
hi = hor[i]
fi = field[i]
curr = hi[-1][i] = w - 1
curc = fi[-1]
for j in WR2:
if fi[j] != curc:
curr = hi[j][i] = j
curc = fi[j]
else:
hi[j][i] = curr
for i in HR:
hi = hor[i]
vi = ver[i]
fi = field[i]
for j in WR:
hij = hi[j]
vij = vi[j]
fij = fi[j]
curr = hij[i]
for k in range(i + 1, h):
if field[k][j] != fij:
break
curr = hij[k] = min(curr, hor[k][j][k])
curr = j
for k in range(h - 1, i - 1, -1):
if hij[k] == -1:
continue
nxtr = hij[k] + 1
dr = nxtr - curr
if dr > 0:
vij[curr:nxtr] = [k] * dr
curr = nxtr
ans = 0
while True:
if hor[0][0][-1] == w - 1:
break
for i in HR:
hi = hor[i]
vi = ver[i]
for j in WR:
hij = hi[j]
vij = vi[j]
# print(ans + 1, i, j, 'first')
# print(hor[i][j])
# print(ver[i][j])
# Update hor using hor, ver using ver
for k in range(i, h):
h_ijk = hij[k]
if h_ijk == -1:
break
if h_ijk == w - 1:
continue
hij[k] = max(h_ijk, hi[h_ijk + 1][k])
for k in range(j, w):
v_ijk = vij[k]
if v_ijk == -1:
break
if v_ijk == h - 1:
continue
vij[k] = max(v_ijk, ver[v_ijk + 1][j][k])
# print(ans + 1, i, j, 'before')
# print(hor[i][j])
# print(ver[i][j])
# Update hor using ver, ver using hor
curr = j
for k in range(h - 1, i - 1, -1):
h_ijk = hij[k]
if h_ijk == -1:
continue
while curr <= h_ijk:
vij[curr] = max(vij[curr], k)
curr += 1
curb = i
for k in range(w - 1, j - 1, -1):
v_ijk = vij[k]
if v_ijk == -1:
continue
while curb <= v_ijk:
hij[curb] = max(hij[curb], k)
curb += 1
# print(ans + 1, i, j, 'after')
# print(hor[i][j])
# print(ver[i][j])
ans += 1
print(ans)
```
| 84,839 |
Provide a correct Python 3 solution for this coding contest problem.
Note the unusual memory limit.
For a rectangular grid where each square is painted white or black, we define its complexity as follows:
* If all the squares are black or all the squares are white, the complexity is 0.
* Otherwise, divide the grid into two subgrids by a line parallel to one of the sides of the grid, and let c_1 and c_2 be the complexities of the subgrids. There can be multiple ways to perform the division, and let m be the minimum value of \max(c_1, c_2) in those divisions. The complexity of the grid is m+1.
You are given a grid with H horizontal rows and W vertical columns where each square is painted white or black. HW characters from A_{11} to A_{HW} represent the colors of the squares. A_{ij} is `#` if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is `.` if that square is white.
Find the complexity of the given grid.
Constraints
* 1 \leq H,W \leq 185
* A_{ij} is `#` or `.`.
Input
Input is given from Standard Input in the following format:
H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}
Output
Print the complexity of the given grid.
Examples
Input
3 3
...
.##
.##
Output
2
Input
6 7
.####.#
....#.
....#.
....#.
.####.#
....##
Output
4
"Correct Solution:
```
H, W = map(int, input().split())
A = [[1 if a == "#" else 0 for a in input()] for _ in range(H)]
X = [[[-2] * (H + 2) for _ in range(W + 2)] for _ in range(H + 2)]
Y = [[[-2] * (W + 2) for _ in range(W + 2)] for _ in range(H + 2)]
for i in range(H):
Xi = X[i]
Yi = Y[i]
for j in range(W):
Xi[j][i] = j
Yi[j][j] = i
for i in range(H):
Xi = X[i]
Ai = A[i]
for j in range(W-1)[::-1]:
if Ai[j] == Ai[j+1]:
Xi[j][i] = Xi[j+1][i]
for i in range(H-1)[::-1]:
Yi = Y[i]
Yi1 = Y[i+1]
Ai = A[i]
Ai1 = A[i+1]
for j in range(W):
if Ai[j] == Ai1[j]:
Yi[j][j] = Yi1[j][j]
for i in range(H):
Xi = X[i]
Ai = A[i]
for j in range(W):
Xij = Xi[j]
for ii in range(i+1, H):
if A[ii][j] != Ai[j]:
break
Xij[ii] = min(Xij[ii-1], X[ii][j][ii])
for i in range(H):
Yi = Y[i]
Ai = A[i]
for j in range(W):
Yij = Yi[j]
for jj in range(j+1, W):
if Ai[jj] != Ai[j]:
break
Yij[jj] = min(Yij[jj-1], Yi[jj][jj])
for k in range(16):
if X[0][0][H-1] == W-1:
print(k)
break
elif k == 15:
print(16)
break
for i in range(H):
Xi = X[i]
Yi = Y[i]
for j in range(W):
Xij = Xi[j]
Yij = Yi[j]
for ii in range(i, H):
Xijii = Xij[ii]
if Xijii >= 0 and X[i][Xijii + 1][ii] >= 0:
Xij[ii] = X[i][Xijii + 1][ii]
for jj in range(j, W):
Yijjj = Yij[jj]
if Yijjj >= 0 and Y[Yijjj + 1][j][jj] >= 0:
Yij[jj] = Y[Yijjj + 1][j][jj]
jj = W - 1
for ii in range(i, H):
while jj >= j and Yij[jj] < ii:
jj -= 1
if jj >= j:
Xij[ii] = max(Xij[ii], jj)
ii = H - 1
for jj in range(j, W):
while ii >= i and Xij[ii] < jj:
ii -= 1
if ii >= i:
Yij[jj] = max(Yij[jj], ii)
```
| 84,840 |
Provide a correct Python 3 solution for this coding contest problem.
Note the unusual memory limit.
For a rectangular grid where each square is painted white or black, we define its complexity as follows:
* If all the squares are black or all the squares are white, the complexity is 0.
* Otherwise, divide the grid into two subgrids by a line parallel to one of the sides of the grid, and let c_1 and c_2 be the complexities of the subgrids. There can be multiple ways to perform the division, and let m be the minimum value of \max(c_1, c_2) in those divisions. The complexity of the grid is m+1.
You are given a grid with H horizontal rows and W vertical columns where each square is painted white or black. HW characters from A_{11} to A_{HW} represent the colors of the squares. A_{ij} is `#` if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is `.` if that square is white.
Find the complexity of the given grid.
Constraints
* 1 \leq H,W \leq 185
* A_{ij} is `#` or `.`.
Input
Input is given from Standard Input in the following format:
H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}
Output
Print the complexity of the given grid.
Examples
Input
3 3
...
.##
.##
Output
2
Input
6 7
.####.#
....#.
....#.
....#.
.####.#
....##
Output
4
"Correct Solution:
```
H, W = map(int, input().split())
A = [[1 if a == "#" else 0 for a in input()] for _ in range(H)]
X = [[[-2] * (H + 2) for _ in range(W + 2)] for _ in range(H + 2)]
Y = [[[-2] * (W + 2) for _ in range(W + 2)] for _ in range(H + 2)]
for i in range(H):
Xi = X[i]
Yi = Y[i]
for j in range(W):
Xi[j][i] = j
Yi[j][j] = i
for i in range(H):
Xi = X[i]
Ai = A[i]
for j in range(W-1)[::-1]:
if Ai[j] == Ai[j+1]:
Xi[j][i] = Xi[j+1][i]
for i in range(H-1)[::-1]:
Yi = Y[i]
Yi1 = Y[i+1]
Ai = A[i]
Ai1 = A[i+1]
for j in range(W):
if Ai[j] == Ai1[j]:
Yi[j][j] = Yi1[j][j]
for i in range(H):
Xi = X[i]
Ai = A[i]
for j in range(W):
Xij = Xi[j]
for ii in range(i+1, H):
if A[ii][j] != Ai[j]:
break
Xij[ii] = min(Xij[ii-1], X[ii][j][ii])
for i in range(H):
Yi = Y[i]
Ai = A[i]
for j in range(W):
Yij = Yi[j]
for jj in range(j+1, W):
if Ai[jj] != Ai[j]:
break
Yij[jj] = min(Yij[jj-1], Yi[jj][jj])
for k in range(16):
if X[0][0][H-1] == W-1:
print(k)
break
elif k == 15:
print(16)
break
for i in range(H):
Xi = X[i]
Yi = Y[i]
for j in range(W):
Xij = Xi[j]
Yij = Yi[j]
for ii in range(i, H):
Xijii = Xij[ii]
if Xijii >= 0 and X[i][Xijii + 1][ii] >= 0:
Xij[ii] = X[i][Xijii + 1][ii]
for jj in range(j, W):
Yijjj = Yij[jj]
if Yijjj >= 0 and Y[Yijjj + 1][j][jj] >= 0:
Yij[jj] = Y[Yijjj + 1][j][jj]
jj = W - 1
for ii in range(i, H):
while jj >= j and Yij[jj] < ii:
jj -= 1
if j <= jj > Xij[ii]:
Xij[ii] = jj
ii = H - 1
for jj in range(j, W):
while ii >= i and Xij[ii] < jj:
ii -= 1
if i <= ii > Yij[jj]:
Yij[jj] = ii
```
| 84,841 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Note the unusual memory limit.
For a rectangular grid where each square is painted white or black, we define its complexity as follows:
* If all the squares are black or all the squares are white, the complexity is 0.
* Otherwise, divide the grid into two subgrids by a line parallel to one of the sides of the grid, and let c_1 and c_2 be the complexities of the subgrids. There can be multiple ways to perform the division, and let m be the minimum value of \max(c_1, c_2) in those divisions. The complexity of the grid is m+1.
You are given a grid with H horizontal rows and W vertical columns where each square is painted white or black. HW characters from A_{11} to A_{HW} represent the colors of the squares. A_{ij} is `#` if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is `.` if that square is white.
Find the complexity of the given grid.
Constraints
* 1 \leq H,W \leq 185
* A_{ij} is `#` or `.`.
Input
Input is given from Standard Input in the following format:
H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}
Output
Print the complexity of the given grid.
Examples
Input
3 3
...
.##
.##
Output
2
Input
6 7
.####.#
....#.
....#.
....#.
.####.#
....##
Output
4
Submitted Solution:
```
from math import ceil
from math import log2
H, W = map( int, input().split())
A = [ input() for _ in range(H)]
T = 0
i = 0
for i in range(H-1):
if A[i] == A[i+1]:
T += 1
S = 0
for i in range(W-1):
check = 1
for k in range(H):
if A[k][i] != A[k][i+1]:
check = 0
break
if check == 1:
S += 1
if H-T == 1:
print(ceil(log2(W-S)))
elif W-S == 1:
print(ceil( log2(H-T)))
elif H-T == 2:
print(2*ceil(log2(W-S)))
elif H-S == 2:
print(ceil( log2(H-T))*2)
else:
print( ceil( log2(H-T+1)-1)*ceil(log2(W-S+1)-1))
```
No
| 84,842 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Note the unusual memory limit.
For a rectangular grid where each square is painted white or black, we define its complexity as follows:
* If all the squares are black or all the squares are white, the complexity is 0.
* Otherwise, divide the grid into two subgrids by a line parallel to one of the sides of the grid, and let c_1 and c_2 be the complexities of the subgrids. There can be multiple ways to perform the division, and let m be the minimum value of \max(c_1, c_2) in those divisions. The complexity of the grid is m+1.
You are given a grid with H horizontal rows and W vertical columns where each square is painted white or black. HW characters from A_{11} to A_{HW} represent the colors of the squares. A_{ij} is `#` if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is `.` if that square is white.
Find the complexity of the given grid.
Constraints
* 1 \leq H,W \leq 185
* A_{ij} is `#` or `.`.
Input
Input is given from Standard Input in the following format:
H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}
Output
Print the complexity of the given grid.
Examples
Input
3 3
...
.##
.##
Output
2
Input
6 7
.####.#
....#.
....#.
....#.
.####.#
....##
Output
4
Submitted Solution:
```
import math
HW=list(map(int, input().split()))
H=HW[0]
W=HW[1]
A=[0]*H
#行列のセット
for i in range(H):
S = input()
dmy = []
for j in range(W):
dmy.append(S[j])
A[i]=dmy
#行の分割数
sep_h=1
for i in range(H-1):
if A[i] != A[i+1]:sep_h+=1
#列の分割数
sep_w=1
for j in range(W-1):
flg=False
for i in range(H):
if A[i][j] !=A [i][j+1]:
flg=True
if flg:sep_w+=1
comp=math.ceil(math.log2(sep_h))+math.ceil(math.log2(sep_w))
print(int(comp))
```
No
| 84,843 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Note the unusual memory limit.
For a rectangular grid where each square is painted white or black, we define its complexity as follows:
* If all the squares are black or all the squares are white, the complexity is 0.
* Otherwise, divide the grid into two subgrids by a line parallel to one of the sides of the grid, and let c_1 and c_2 be the complexities of the subgrids. There can be multiple ways to perform the division, and let m be the minimum value of \max(c_1, c_2) in those divisions. The complexity of the grid is m+1.
You are given a grid with H horizontal rows and W vertical columns where each square is painted white or black. HW characters from A_{11} to A_{HW} represent the colors of the squares. A_{ij} is `#` if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is `.` if that square is white.
Find the complexity of the given grid.
Constraints
* 1 \leq H,W \leq 185
* A_{ij} is `#` or `.`.
Input
Input is given from Standard Input in the following format:
H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}
Output
Print the complexity of the given grid.
Examples
Input
3 3
...
.##
.##
Output
2
Input
6 7
.####.#
....#.
....#.
....#.
.####.#
....##
Output
4
Submitted Solution:
```
import math
N = int(input())
result = 0
root = math.ceil(math.sqrt(N))
for i in range(root):
if N % (i + 1) == 0:
result += N / (i + 1) - 1
print(result)
```
No
| 84,844 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Note the unusual memory limit.
For a rectangular grid where each square is painted white or black, we define its complexity as follows:
* If all the squares are black or all the squares are white, the complexity is 0.
* Otherwise, divide the grid into two subgrids by a line parallel to one of the sides of the grid, and let c_1 and c_2 be the complexities of the subgrids. There can be multiple ways to perform the division, and let m be the minimum value of \max(c_1, c_2) in those divisions. The complexity of the grid is m+1.
You are given a grid with H horizontal rows and W vertical columns where each square is painted white or black. HW characters from A_{11} to A_{HW} represent the colors of the squares. A_{ij} is `#` if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is `.` if that square is white.
Find the complexity of the given grid.
Constraints
* 1 \leq H,W \leq 185
* A_{ij} is `#` or `.`.
Input
Input is given from Standard Input in the following format:
H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}
Output
Print the complexity of the given grid.
Examples
Input
3 3
...
.##
.##
Output
2
Input
6 7
.####.#
....#.
....#.
....#.
.####.#
....##
Output
4
Submitted Solution:
```
h, w = map(int, input().split())
G = []
for i in range(h):
G.append(input())
dp = [0 for i in range(h)]
for i in range(h):
cnt = 0
for j in range(w-1):
if G[i][j+1] != G[i][j]:
cnt += 1
if i == 0:
dp[i] = cnt
elif i > 0 and G[i] == G[i-1]:
dp[i] = dp[i-1]
else:
dp[i] = max(dp[i-1], cnt+1)
print(dp[-1])
```
No
| 84,845 |
Provide a correct Python 3 solution for this coding contest problem.
There are N Reversi pieces arranged in a row. (A Reversi piece is a disc with a black side and a white side.) The state of each piece is represented by a string S of length N. If S_i=`B`, the i-th piece from the left is showing black; If S_i=`W`, the i-th piece from the left is showing white.
Consider performing the following operation:
* Choose i (1 \leq i < N) such that the i-th piece from the left is showing black and the (i+1)-th piece from the left is showing white, then flip both of those pieces. That is, the i-th piece from the left is now showing white and the (i+1)-th piece from the left is now showing black.
Find the maximum possible number of times this operation can be performed.
Constraints
* 1 \leq |S| \leq 2\times 10^5
* S_i=`B` or `W`
Input
Input is given from Standard Input in the following format:
S
Output
Print the maximum possible number of times the operation can be performed.
Examples
Input
BBW
Output
2
Input
BWBWBW
Output
6
"Correct Solution:
```
S = input()
ans, cnt = 0, 0
for i in range(len(S)):
if S[i] == "W":
ans += i - cnt
cnt += 1
print(ans)
```
| 84,846 |
Provide a correct Python 3 solution for this coding contest problem.
There are N Reversi pieces arranged in a row. (A Reversi piece is a disc with a black side and a white side.) The state of each piece is represented by a string S of length N. If S_i=`B`, the i-th piece from the left is showing black; If S_i=`W`, the i-th piece from the left is showing white.
Consider performing the following operation:
* Choose i (1 \leq i < N) such that the i-th piece from the left is showing black and the (i+1)-th piece from the left is showing white, then flip both of those pieces. That is, the i-th piece from the left is now showing white and the (i+1)-th piece from the left is now showing black.
Find the maximum possible number of times this operation can be performed.
Constraints
* 1 \leq |S| \leq 2\times 10^5
* S_i=`B` or `W`
Input
Input is given from Standard Input in the following format:
S
Output
Print the maximum possible number of times the operation can be performed.
Examples
Input
BBW
Output
2
Input
BWBWBW
Output
6
"Correct Solution:
```
S = input()
r = 0
nB = 0
for c in S:
if c == "B":
nB += 1
if c == "W":
r += nB
print(r)
```
| 84,847 |
Provide a correct Python 3 solution for this coding contest problem.
There are N Reversi pieces arranged in a row. (A Reversi piece is a disc with a black side and a white side.) The state of each piece is represented by a string S of length N. If S_i=`B`, the i-th piece from the left is showing black; If S_i=`W`, the i-th piece from the left is showing white.
Consider performing the following operation:
* Choose i (1 \leq i < N) such that the i-th piece from the left is showing black and the (i+1)-th piece from the left is showing white, then flip both of those pieces. That is, the i-th piece from the left is now showing white and the (i+1)-th piece from the left is now showing black.
Find the maximum possible number of times this operation can be performed.
Constraints
* 1 \leq |S| \leq 2\times 10^5
* S_i=`B` or `W`
Input
Input is given from Standard Input in the following format:
S
Output
Print the maximum possible number of times the operation can be performed.
Examples
Input
BBW
Output
2
Input
BWBWBW
Output
6
"Correct Solution:
```
cnt = ans = 0
for c in input():
if c is 'W':
ans += cnt
else:
cnt += 1
print(ans)
```
| 84,848 |
Provide a correct Python 3 solution for this coding contest problem.
There are N Reversi pieces arranged in a row. (A Reversi piece is a disc with a black side and a white side.) The state of each piece is represented by a string S of length N. If S_i=`B`, the i-th piece from the left is showing black; If S_i=`W`, the i-th piece from the left is showing white.
Consider performing the following operation:
* Choose i (1 \leq i < N) such that the i-th piece from the left is showing black and the (i+1)-th piece from the left is showing white, then flip both of those pieces. That is, the i-th piece from the left is now showing white and the (i+1)-th piece from the left is now showing black.
Find the maximum possible number of times this operation can be performed.
Constraints
* 1 \leq |S| \leq 2\times 10^5
* S_i=`B` or `W`
Input
Input is given from Standard Input in the following format:
S
Output
Print the maximum possible number of times the operation can be performed.
Examples
Input
BBW
Output
2
Input
BWBWBW
Output
6
"Correct Solution:
```
S=input()
k=0
ans=0
for i in range(len(S)):
if S[i]=="W":
ans+=i-k
k+=1
print(ans)
```
| 84,849 |
Provide a correct Python 3 solution for this coding contest problem.
There are N Reversi pieces arranged in a row. (A Reversi piece is a disc with a black side and a white side.) The state of each piece is represented by a string S of length N. If S_i=`B`, the i-th piece from the left is showing black; If S_i=`W`, the i-th piece from the left is showing white.
Consider performing the following operation:
* Choose i (1 \leq i < N) such that the i-th piece from the left is showing black and the (i+1)-th piece from the left is showing white, then flip both of those pieces. That is, the i-th piece from the left is now showing white and the (i+1)-th piece from the left is now showing black.
Find the maximum possible number of times this operation can be performed.
Constraints
* 1 \leq |S| \leq 2\times 10^5
* S_i=`B` or `W`
Input
Input is given from Standard Input in the following format:
S
Output
Print the maximum possible number of times the operation can be performed.
Examples
Input
BBW
Output
2
Input
BWBWBW
Output
6
"Correct Solution:
```
S=input()
ans=0
b_cnt=0
for i in range(len(S)):
if S[i]=="B":
b_cnt+=1
else:
ans+=b_cnt
print(ans)
```
| 84,850 |
Provide a correct Python 3 solution for this coding contest problem.
There are N Reversi pieces arranged in a row. (A Reversi piece is a disc with a black side and a white side.) The state of each piece is represented by a string S of length N. If S_i=`B`, the i-th piece from the left is showing black; If S_i=`W`, the i-th piece from the left is showing white.
Consider performing the following operation:
* Choose i (1 \leq i < N) such that the i-th piece from the left is showing black and the (i+1)-th piece from the left is showing white, then flip both of those pieces. That is, the i-th piece from the left is now showing white and the (i+1)-th piece from the left is now showing black.
Find the maximum possible number of times this operation can be performed.
Constraints
* 1 \leq |S| \leq 2\times 10^5
* S_i=`B` or `W`
Input
Input is given from Standard Input in the following format:
S
Output
Print the maximum possible number of times the operation can be performed.
Examples
Input
BBW
Output
2
Input
BWBWBW
Output
6
"Correct Solution:
```
S=list(input())
c=0
ans=0
for i in range(len(S)):
if S[i]=='W':
ans+=i-c
c+=1
print(ans)
```
| 84,851 |
Provide a correct Python 3 solution for this coding contest problem.
There are N Reversi pieces arranged in a row. (A Reversi piece is a disc with a black side and a white side.) The state of each piece is represented by a string S of length N. If S_i=`B`, the i-th piece from the left is showing black; If S_i=`W`, the i-th piece from the left is showing white.
Consider performing the following operation:
* Choose i (1 \leq i < N) such that the i-th piece from the left is showing black and the (i+1)-th piece from the left is showing white, then flip both of those pieces. That is, the i-th piece from the left is now showing white and the (i+1)-th piece from the left is now showing black.
Find the maximum possible number of times this operation can be performed.
Constraints
* 1 \leq |S| \leq 2\times 10^5
* S_i=`B` or `W`
Input
Input is given from Standard Input in the following format:
S
Output
Print the maximum possible number of times the operation can be performed.
Examples
Input
BBW
Output
2
Input
BWBWBW
Output
6
"Correct Solution:
```
S = input()
k1 = k2 = 0
for i in S[::-1]:
if i == 'W':
k2 += 1
else:
k1 += k2
print(k1)
```
| 84,852 |
Provide a correct Python 3 solution for this coding contest problem.
There are N Reversi pieces arranged in a row. (A Reversi piece is a disc with a black side and a white side.) The state of each piece is represented by a string S of length N. If S_i=`B`, the i-th piece from the left is showing black; If S_i=`W`, the i-th piece from the left is showing white.
Consider performing the following operation:
* Choose i (1 \leq i < N) such that the i-th piece from the left is showing black and the (i+1)-th piece from the left is showing white, then flip both of those pieces. That is, the i-th piece from the left is now showing white and the (i+1)-th piece from the left is now showing black.
Find the maximum possible number of times this operation can be performed.
Constraints
* 1 \leq |S| \leq 2\times 10^5
* S_i=`B` or `W`
Input
Input is given from Standard Input in the following format:
S
Output
Print the maximum possible number of times the operation can be performed.
Examples
Input
BBW
Output
2
Input
BWBWBW
Output
6
"Correct Solution:
```
s = list(input())
c = 0
ans = 0
for i in s:
if i == "B":
c += 1
else:
ans += c
print(ans)
```
| 84,853 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N Reversi pieces arranged in a row. (A Reversi piece is a disc with a black side and a white side.) The state of each piece is represented by a string S of length N. If S_i=`B`, the i-th piece from the left is showing black; If S_i=`W`, the i-th piece from the left is showing white.
Consider performing the following operation:
* Choose i (1 \leq i < N) such that the i-th piece from the left is showing black and the (i+1)-th piece from the left is showing white, then flip both of those pieces. That is, the i-th piece from the left is now showing white and the (i+1)-th piece from the left is now showing black.
Find the maximum possible number of times this operation can be performed.
Constraints
* 1 \leq |S| \leq 2\times 10^5
* S_i=`B` or `W`
Input
Input is given from Standard Input in the following format:
S
Output
Print the maximum possible number of times the operation can be performed.
Examples
Input
BBW
Output
2
Input
BWBWBW
Output
6
Submitted Solution:
```
S = input()
b = 0
ans = 0
for c in S:
if c == 'B':
b += 1
else:
ans += b
print(ans)
```
Yes
| 84,854 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N Reversi pieces arranged in a row. (A Reversi piece is a disc with a black side and a white side.) The state of each piece is represented by a string S of length N. If S_i=`B`, the i-th piece from the left is showing black; If S_i=`W`, the i-th piece from the left is showing white.
Consider performing the following operation:
* Choose i (1 \leq i < N) such that the i-th piece from the left is showing black and the (i+1)-th piece from the left is showing white, then flip both of those pieces. That is, the i-th piece from the left is now showing white and the (i+1)-th piece from the left is now showing black.
Find the maximum possible number of times this operation can be performed.
Constraints
* 1 \leq |S| \leq 2\times 10^5
* S_i=`B` or `W`
Input
Input is given from Standard Input in the following format:
S
Output
Print the maximum possible number of times the operation can be performed.
Examples
Input
BBW
Output
2
Input
BWBWBW
Output
6
Submitted Solution:
```
s = input()
ans = b = 0
for i in s:
if i=='W':ans+=b
else:b+=1
print(ans)
```
Yes
| 84,855 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N Reversi pieces arranged in a row. (A Reversi piece is a disc with a black side and a white side.) The state of each piece is represented by a string S of length N. If S_i=`B`, the i-th piece from the left is showing black; If S_i=`W`, the i-th piece from the left is showing white.
Consider performing the following operation:
* Choose i (1 \leq i < N) such that the i-th piece from the left is showing black and the (i+1)-th piece from the left is showing white, then flip both of those pieces. That is, the i-th piece from the left is now showing white and the (i+1)-th piece from the left is now showing black.
Find the maximum possible number of times this operation can be performed.
Constraints
* 1 \leq |S| \leq 2\times 10^5
* S_i=`B` or `W`
Input
Input is given from Standard Input in the following format:
S
Output
Print the maximum possible number of times the operation can be performed.
Examples
Input
BBW
Output
2
Input
BWBWBW
Output
6
Submitted Solution:
```
s=input()
c=0
a=0
for i in range(len(s)):
if s[i]=="W":a+=i-c;c+=1
print(a)
```
Yes
| 84,856 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N Reversi pieces arranged in a row. (A Reversi piece is a disc with a black side and a white side.) The state of each piece is represented by a string S of length N. If S_i=`B`, the i-th piece from the left is showing black; If S_i=`W`, the i-th piece from the left is showing white.
Consider performing the following operation:
* Choose i (1 \leq i < N) such that the i-th piece from the left is showing black and the (i+1)-th piece from the left is showing white, then flip both of those pieces. That is, the i-th piece from the left is now showing white and the (i+1)-th piece from the left is now showing black.
Find the maximum possible number of times this operation can be performed.
Constraints
* 1 \leq |S| \leq 2\times 10^5
* S_i=`B` or `W`
Input
Input is given from Standard Input in the following format:
S
Output
Print the maximum possible number of times the operation can be performed.
Examples
Input
BBW
Output
2
Input
BWBWBW
Output
6
Submitted Solution:
```
s=input()
n_s=s.count('W')
a=0
for i in range(len(s)):
if s[i]=='W':
a+=i+1
print(a-sum(range(n_s+1)))
```
Yes
| 84,857 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N Reversi pieces arranged in a row. (A Reversi piece is a disc with a black side and a white side.) The state of each piece is represented by a string S of length N. If S_i=`B`, the i-th piece from the left is showing black; If S_i=`W`, the i-th piece from the left is showing white.
Consider performing the following operation:
* Choose i (1 \leq i < N) such that the i-th piece from the left is showing black and the (i+1)-th piece from the left is showing white, then flip both of those pieces. That is, the i-th piece from the left is now showing white and the (i+1)-th piece from the left is now showing black.
Find the maximum possible number of times this operation can be performed.
Constraints
* 1 \leq |S| \leq 2\times 10^5
* S_i=`B` or `W`
Input
Input is given from Standard Input in the following format:
S
Output
Print the maximum possible number of times the operation can be performed.
Examples
Input
BBW
Output
2
Input
BWBWBW
Output
6
Submitted Solution:
```
s = input()
cnt = 0
for i in range(len(s)):
if s[i] == "B":
cnt += s[i:].count("W")
print(cnt)
```
No
| 84,858 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N Reversi pieces arranged in a row. (A Reversi piece is a disc with a black side and a white side.) The state of each piece is represented by a string S of length N. If S_i=`B`, the i-th piece from the left is showing black; If S_i=`W`, the i-th piece from the left is showing white.
Consider performing the following operation:
* Choose i (1 \leq i < N) such that the i-th piece from the left is showing black and the (i+1)-th piece from the left is showing white, then flip both of those pieces. That is, the i-th piece from the left is now showing white and the (i+1)-th piece from the left is now showing black.
Find the maximum possible number of times this operation can be performed.
Constraints
* 1 \leq |S| \leq 2\times 10^5
* S_i=`B` or `W`
Input
Input is given from Standard Input in the following format:
S
Output
Print the maximum possible number of times the operation can be performed.
Examples
Input
BBW
Output
2
Input
BWBWBW
Output
6
Submitted Solution:
```
s = list(input())
cnt = 0
ans = 0
while True:
if 'W' not in s:
break
for i in range(len(s)):
if s[i] == 'B':
cnt += 1
else:
ans += cnt
cnt = 0
s.pop(i)
break
print(ans)
```
No
| 84,859 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N Reversi pieces arranged in a row. (A Reversi piece is a disc with a black side and a white side.) The state of each piece is represented by a string S of length N. If S_i=`B`, the i-th piece from the left is showing black; If S_i=`W`, the i-th piece from the left is showing white.
Consider performing the following operation:
* Choose i (1 \leq i < N) such that the i-th piece from the left is showing black and the (i+1)-th piece from the left is showing white, then flip both of those pieces. That is, the i-th piece from the left is now showing white and the (i+1)-th piece from the left is now showing black.
Find the maximum possible number of times this operation can be performed.
Constraints
* 1 \leq |S| \leq 2\times 10^5
* S_i=`B` or `W`
Input
Input is given from Standard Input in the following format:
S
Output
Print the maximum possible number of times the operation can be performed.
Examples
Input
BBW
Output
2
Input
BWBWBW
Output
6
Submitted Solution:
```
S = input()
flag = False
cnt = 0
l = 0
for i in range(len(S)):
if S[i] == 'B' and flag == False:
flag = True
if S[i] == 'W' and flag:
cnt += i - l
l += 1
print(cnt)
```
No
| 84,860 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N Reversi pieces arranged in a row. (A Reversi piece is a disc with a black side and a white side.) The state of each piece is represented by a string S of length N. If S_i=`B`, the i-th piece from the left is showing black; If S_i=`W`, the i-th piece from the left is showing white.
Consider performing the following operation:
* Choose i (1 \leq i < N) such that the i-th piece from the left is showing black and the (i+1)-th piece from the left is showing white, then flip both of those pieces. That is, the i-th piece from the left is now showing white and the (i+1)-th piece from the left is now showing black.
Find the maximum possible number of times this operation can be performed.
Constraints
* 1 \leq |S| \leq 2\times 10^5
* S_i=`B` or `W`
Input
Input is given from Standard Input in the following format:
S
Output
Print the maximum possible number of times the operation can be performed.
Examples
Input
BBW
Output
2
Input
BWBWBW
Output
6
Submitted Solution:
```
S = list(input())
count = 0
for i in range(len(S)):
for j in range(len(S)-1, i, -1):
if S[j] == "W" and S[j-1] == "B":
S[j], S[j-1] = S[j-1], S[j]
count += 1
print(count)
```
No
| 84,861 |
Provide a correct Python 3 solution for this coding contest problem.
There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.
You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.
* Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq N)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.
Examples
Input
4
0
1
1
2
Output
3
Input
3
1
2
1
Output
-1
Input
9
0
1
1
0
1
2
2
1
2
Output
8
"Correct Solution:
```
N = int(input())
A = [int(input()) for _ in range(N)]
if A[0]:
print(-1)
exit()
ans = 0
dp = A[-1]
for a, b in zip(A[-2::-1], A[-1::-1]):
if a == b - 1:
continue
elif a >= b:
ans += dp
dp = a
else:
print(-1)
exit()
print(ans + dp)
```
| 84,862 |
Provide a correct Python 3 solution for this coding contest problem.
There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.
You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.
* Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq N)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.
Examples
Input
4
0
1
1
2
Output
3
Input
3
1
2
1
Output
-1
Input
9
0
1
1
0
1
2
2
1
2
Output
8
"Correct Solution:
```
n = int(input())
a = [int(input()) for i in range(n)]
def check():
globals()
s = 0
if a[0]!=0:
return -1
for i in range(n-1):
if a[i+1]<=a[i]:
s+=a[i]
if a[i+1]>a[i]+1:
return -1
return s+a[-1]
print(check())
```
| 84,863 |
Provide a correct Python 3 solution for this coding contest problem.
There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.
You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.
* Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq N)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.
Examples
Input
4
0
1
1
2
Output
3
Input
3
1
2
1
Output
-1
Input
9
0
1
1
0
1
2
2
1
2
Output
8
"Correct Solution:
```
N = int(input())
ans = 0
L = []
isok = True
for i in range(N):
n = int(input())
if n>i: isok = False
L.append(n)
for i in range(N-1):
if L[i+1] <= L[i]:
ans += L[i+1]
elif L[i+1] == L[i]+1:
ans += 1
elif L[i+1] > L[i]:
isok=False
break
if isok:
print(ans)
else:
print(-1)
```
| 84,864 |
Provide a correct Python 3 solution for this coding contest problem.
There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.
You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.
* Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq N)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.
Examples
Input
4
0
1
1
2
Output
3
Input
3
1
2
1
Output
-1
Input
9
0
1
1
0
1
2
2
1
2
Output
8
"Correct Solution:
```
n=int(input())
a=[int(input())for i in range(n)]
x,y=-1,-1
for i in a:
if i-x>1:print(-1);exit()
elif i==x+1:y+=1
else:y+=i
x=i
print(y)
```
| 84,865 |
Provide a correct Python 3 solution for this coding contest problem.
There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.
You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.
* Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq N)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.
Examples
Input
4
0
1
1
2
Output
3
Input
3
1
2
1
Output
-1
Input
9
0
1
1
0
1
2
2
1
2
Output
8
"Correct Solution:
```
import sys
input = sys.stdin.readline
cur = -1
c = 0
for i in range(int(input())):
pre,cur = cur,int(input())
if cur == 0:
continue
elif cur == pre + 1:
c += 1
elif cur <= pre:
c += cur
else:
print(-1)
exit()
print(c)
```
| 84,866 |
Provide a correct Python 3 solution for this coding contest problem.
There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.
You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.
* Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq N)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.
Examples
Input
4
0
1
1
2
Output
3
Input
3
1
2
1
Output
-1
Input
9
0
1
1
0
1
2
2
1
2
Output
8
"Correct Solution:
```
n = int(input())
A = [int(input())for _ in range(n)]
if A[0] != 0:
print(-1)
exit()
ans = A[-1]
for a, prev_a in reversed(tuple(zip(A, A[1:]))):
if a == prev_a-1:
continue
if a < prev_a-1:
print(-1)
break
ans += a
else:
print(ans)
```
| 84,867 |
Provide a correct Python 3 solution for this coding contest problem.
There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.
You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.
* Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq N)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.
Examples
Input
4
0
1
1
2
Output
3
Input
3
1
2
1
Output
-1
Input
9
0
1
1
0
1
2
2
1
2
Output
8
"Correct Solution:
```
N = int(input())
A = [int(input()) for _ in range(N)]
ok = True
pre = -1
for i, a in enumerate(A):
if a > pre + 1:
ok = False
break
pre = a
if not ok:
print(-1)
else:
c = 0
for i in range(N-1):
if A[i+1] != A[i] + 1:
c += A[i+1]
else:
c += 1
print(c)
```
| 84,868 |
Provide a correct Python 3 solution for this coding contest problem.
There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.
You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.
* Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq N)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.
Examples
Input
4
0
1
1
2
Output
3
Input
3
1
2
1
Output
-1
Input
9
0
1
1
0
1
2
2
1
2
Output
8
"Correct Solution:
```
n = int(input())
a = [int(input()) for _i in range(n)] + [-1]
result = -1
for i in range(n):
if a[i-1] == a[i]:
result += a[i]
elif a[i-1] + 1 == a[i]:
result += 1
elif a[i-1] > a[i]:
result += a[i]
else:
result = -1
break
print(result)
```
| 84,869 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.
You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.
* Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq N)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.
Examples
Input
4
0
1
1
2
Output
3
Input
3
1
2
1
Output
-1
Input
9
0
1
1
0
1
2
2
1
2
Output
8
Submitted Solution:
```
import sys
#sys.stdin=open("data.txt")
input=sys.stdin.readline
n=int(input())
a=[int(input()) for _ in range(n)]
bad=(a[0]!=0)
for i in range(n-1):
if a[i]+1<a[i+1]:
bad=True
if bad: print(-1)
else:
# calculate answer
ans=[0]*n
for i in range(n):
ans[i-a[i]]=a[i]
print(sum(ans))
```
Yes
| 84,870 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.
You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.
* Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq N)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.
Examples
Input
4
0
1
1
2
Output
3
Input
3
1
2
1
Output
-1
Input
9
0
1
1
0
1
2
2
1
2
Output
8
Submitted Solution:
```
N = int(input())
ans = 0
arr = [-1]
for i in range(N):
A = int(input())
if A > arr[i] + 1:
print(-1)
break
if A == arr[i] + 1 and i != 0:
ans += 1
else:
ans += A
arr.append(A)
else:
print(ans)
```
Yes
| 84,871 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.
You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.
* Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq N)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.
Examples
Input
4
0
1
1
2
Output
3
Input
3
1
2
1
Output
-1
Input
9
0
1
1
0
1
2
2
1
2
Output
8
Submitted Solution:
```
N = int(input())
A = [int(input()) for _ in range(N)]
if A[0] > 0:
print(-1)
else:
ans = 0
for n in range(N-1, -1, -1):
if A[n] - A[n-1] > 1 or A[n] > n:
print(-1)
break
else:
if A[n] - A[n-1] == 1:
ans += 1
else:
ans += A[n]
else:
print(ans)
```
Yes
| 84,872 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.
You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.
* Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq N)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.
Examples
Input
4
0
1
1
2
Output
3
Input
3
1
2
1
Output
-1
Input
9
0
1
1
0
1
2
2
1
2
Output
8
Submitted Solution:
```
n = int(input())
ans = -1
prev = -1
for _ in range(n):
a = int(input())
if prev+1 == a:
prev = a
ans += 1
continue
if prev+1 < a:
print(-1)
break
ans += a
prev = a
else:
print(ans)
```
Yes
| 84,873 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.
You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.
* Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq N)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.
Examples
Input
4
0
1
1
2
Output
3
Input
3
1
2
1
Output
-1
Input
9
0
1
1
0
1
2
2
1
2
Output
8
Submitted Solution:
```
import bisect, collections, copy, heapq, itertools, math, string, sys
input = lambda: sys.stdin.readline().rstrip()
sys.setrecursionlimit(10**7)
INF = float('inf')
def I(): return int(input())
def F(): return float(input())
def SS(): return input()
def LI(): return [int(x) for x in input().split()]
def LI_(): return [int(x)-1 for x in input().split()]
def LF(): return [float(x) for x in input().split()]
def LSS(): return input().split()
def resolve():
N = I()
A = [I() for _ in range(N)]
is_ok = True
# A[0]!=0か、A[i]+1 < A[i+1]があるとダメ
if A[0] != 0:
is_ok = False
else:
for i in range(N - 1):
if A[i] + 1 < A[i+1]:
is_ok = False
break
ans = len([i for i in A if i > 0])
if is_ok:
# A[i] >= A[i+1] >= 2のとき、余計に1手
for i in range(N - 1):
if A[i] >= A[i+1] >= 2:
ans += 1
if is_ok:
print(ans)
else:
print(-1)
if __name__ == '__main__':
resolve()
```
No
| 84,874 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.
You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.
* Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq N)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.
Examples
Input
4
0
1
1
2
Output
3
Input
3
1
2
1
Output
-1
Input
9
0
1
1
0
1
2
2
1
2
Output
8
Submitted Solution:
```
n = int(input())
a = [int(input()) for _ in range(n)]
for i in range(1,n):
if a[i]-a[i-1] > 1:
print(-1)
exit(0)
cnt = 0
cur = 0
for i in range(n-1,-1,-1):
if cur < a[i]:
cur = a[i]
cnt += a[i]
if cur:
cur -= 1
print(cnt)
```
No
| 84,875 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.
You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.
* Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq N)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.
Examples
Input
4
0
1
1
2
Output
3
Input
3
1
2
1
Output
-1
Input
9
0
1
1
0
1
2
2
1
2
Output
8
Submitted Solution:
```
def main():
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
from collections import Counter, deque
from collections import defaultdict
from itertools import combinations, permutations, accumulate, groupby, product
from bisect import bisect_left,bisect_right
from heapq import heapify, heappop, heappush
from math import floor, ceil,pi,factorial
from operator import itemgetter
def I(): return int(input())
def MI(): return map(int, input().split())
def LI(): return list(map(int, input().split()))
def LI2(): return [int(input()) for i in range(n)]
def MXI(): return [[LI()]for i in range(n)]
def SI(): return input().rstrip()
def printns(x): print('\n'.join(x))
def printni(x): print('\n'.join(list(map(str,x))))
inf = 10**17
mod = 10**9 + 7
#main code here!
n=I()
lis=LI2()
ind=[i for i in range(n)]
if lis[0]!=0:
print(-1)
sys.exit()
for i in range(1,n):
if lis[i]==0:
ind[i]=0
else:
ind[i]=ind[i-1]+1
for i in range(n):
if lis[i]>ind[i]:
print(-1)
sys.exit()
ans=0
mem=0
'''for i in range(n):
j=n-i-1
u=lis[j]
if lis[j-1]!=lis[j]-1:
ans+=u
ans+=mem
mem=0
else:
mem=lis[j]'''
for i in range(n-1):
x=lis[i]
if lis[i+1]==lis[i]+1:
continue
else:
ans+=x
if n!=1 and lis[-1]==lis[-2]+1:
ans+=lis[-1]
print(ans)
if __name__=="__main__":
main()
```
No
| 84,876 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.
You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.
* Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.
Constraints
* 1 \leq N \leq 2 \times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq N)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.
Examples
Input
4
0
1
1
2
Output
3
Input
3
1
2
1
Output
-1
Input
9
0
1
1
0
1
2
2
1
2
Output
8
Submitted Solution:
```
n = int(input())
a = [int(input()) for i in range(n)]
ans,flag = 0,True
for i in range(n-1):
if a[i]+1==a[i+1]: ans+=1
elif a[i]>=a[i+1]: ans+=a[i+1]
else:
flag = False
break
if flag: print(ans)
else: print(-1)
```
No
| 84,877 |
Provide a correct Python 3 solution for this coding contest problem.
In your garden, there is a long and narrow flowerbed that stretches infinitely to the east. You have decided to plant N kinds of flowers in this empty flowerbed. For convenience, we will call these N kinds of flowers Flower 1, 2, …, N. Also, we will call the position that is p centimeters from the west end of the flowerbed Position p.
You will plant Flower i (1 ≤ i ≤ N) as follows: first, plant one at Position w_i, then plant one every d_i centimeters endlessly toward the east. That is, Flower i will be planted at the positions w_i, w_i + d_i, w_i + 2 d_i, … Note that more than one flower may be planted at the same position.
Find the position at which the K-th flower from the west is planted. If more than one flower is planted at the same position, they are counted individually.
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ K ≤ 10^9
* 1 ≤ w_i ≤ 10^{18}
* 1 ≤ d_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
w_1 d_1
:
w_N d_N
Output
When the K-th flower from the west is planted at Position X, print the value of X. (The westmost flower is counted as the 1-st flower.)
Examples
Input
2 6
20 10
25 15
Output
50
Input
3 9
10 10
10 10
10 10
Output
30
Input
1 1000000000
1000000000000000000 1000000000
Output
1999999999000000000
"Correct Solution:
```
def count(N, x, w, d):
cnt = 0
for i in range(N):
if x >= w[i]:
cnt += (x - w[i]) // d[i] + 1
return cnt
def main():
N, K = map(int, input().split())
w = [0] * N
d = [0] * N
for i in range(N):
w[i], d[i] = map(int, input().split())
lo = 0
hi = max(w) + max(d) * (K-1)
while lo < hi:
mid = (lo + hi) // 2
if count(N, mid, w, d) < K:
lo = mid + 1
else:
hi = mid
print(lo)
if __name__ == "__main__":
main()
```
| 84,878 |
Provide a correct Python 3 solution for this coding contest problem.
In your garden, there is a long and narrow flowerbed that stretches infinitely to the east. You have decided to plant N kinds of flowers in this empty flowerbed. For convenience, we will call these N kinds of flowers Flower 1, 2, …, N. Also, we will call the position that is p centimeters from the west end of the flowerbed Position p.
You will plant Flower i (1 ≤ i ≤ N) as follows: first, plant one at Position w_i, then plant one every d_i centimeters endlessly toward the east. That is, Flower i will be planted at the positions w_i, w_i + d_i, w_i + 2 d_i, … Note that more than one flower may be planted at the same position.
Find the position at which the K-th flower from the west is planted. If more than one flower is planted at the same position, they are counted individually.
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ K ≤ 10^9
* 1 ≤ w_i ≤ 10^{18}
* 1 ≤ d_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
w_1 d_1
:
w_N d_N
Output
When the K-th flower from the west is planted at Position X, print the value of X. (The westmost flower is counted as the 1-st flower.)
Examples
Input
2 6
20 10
25 15
Output
50
Input
3 9
10 10
10 10
10 10
Output
30
Input
1 1000000000
1000000000000000000 1000000000
Output
1999999999000000000
"Correct Solution:
```
import sys
input = sys.stdin.buffer.readline
sys.setrecursionlimit(10 ** 7)
N, K = map(int, input().split())
WD = tuple(tuple(map(int, input().split())) for _ in range(N))
l = 0
r = 2 * 10 ** 18 + 100
while (r - l) > 1:
pos = (r + l) // 2
cnt = 0
for w, d in WD:
if pos < w:
continue
cnt += 1 + (pos - w) // d
if cnt >= K:
r = pos
else:
l = pos
print(r)
```
| 84,879 |
Provide a correct Python 3 solution for this coding contest problem.
In your garden, there is a long and narrow flowerbed that stretches infinitely to the east. You have decided to plant N kinds of flowers in this empty flowerbed. For convenience, we will call these N kinds of flowers Flower 1, 2, …, N. Also, we will call the position that is p centimeters from the west end of the flowerbed Position p.
You will plant Flower i (1 ≤ i ≤ N) as follows: first, plant one at Position w_i, then plant one every d_i centimeters endlessly toward the east. That is, Flower i will be planted at the positions w_i, w_i + d_i, w_i + 2 d_i, … Note that more than one flower may be planted at the same position.
Find the position at which the K-th flower from the west is planted. If more than one flower is planted at the same position, they are counted individually.
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ K ≤ 10^9
* 1 ≤ w_i ≤ 10^{18}
* 1 ≤ d_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
w_1 d_1
:
w_N d_N
Output
When the K-th flower from the west is planted at Position X, print the value of X. (The westmost flower is counted as the 1-st flower.)
Examples
Input
2 6
20 10
25 15
Output
50
Input
3 9
10 10
10 10
10 10
Output
30
Input
1 1000000000
1000000000000000000 1000000000
Output
1999999999000000000
"Correct Solution:
```
from bisect import bisect
def solve(l, r):
if l > r:
return l
m = (l + r) // 2
j = bisect(flowers, (m, float('inf')))
t = sum((m - w) // d + 1 for w, d in flowers[:j])
if t < k:
l = m + 1
else:
r = m - 1
return solve(l, r)
n, k = map(int, input().split())
flowers = [tuple(map(int, input().split())) for _ in range(n)]
flowers.sort()
print(solve(1, flowers[0][0] + flowers[0][1] * k))
```
| 84,880 |
Provide a correct Python 3 solution for this coding contest problem.
In your garden, there is a long and narrow flowerbed that stretches infinitely to the east. You have decided to plant N kinds of flowers in this empty flowerbed. For convenience, we will call these N kinds of flowers Flower 1, 2, …, N. Also, we will call the position that is p centimeters from the west end of the flowerbed Position p.
You will plant Flower i (1 ≤ i ≤ N) as follows: first, plant one at Position w_i, then plant one every d_i centimeters endlessly toward the east. That is, Flower i will be planted at the positions w_i, w_i + d_i, w_i + 2 d_i, … Note that more than one flower may be planted at the same position.
Find the position at which the K-th flower from the west is planted. If more than one flower is planted at the same position, they are counted individually.
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ K ≤ 10^9
* 1 ≤ w_i ≤ 10^{18}
* 1 ≤ d_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
w_1 d_1
:
w_N d_N
Output
When the K-th flower from the west is planted at Position X, print the value of X. (The westmost flower is counted as the 1-st flower.)
Examples
Input
2 6
20 10
25 15
Output
50
Input
3 9
10 10
10 10
10 10
Output
30
Input
1 1000000000
1000000000000000000 1000000000
Output
1999999999000000000
"Correct Solution:
```
import sys
input = sys.stdin.readline
N, K = map(int, input().split())
a = []
for _ in range(N):
w, d = map(int, input().split())
a.append((w, d))
def check(x):
res = 0
for t in a:
w, d = t
res += max(0, x - w) // d + int(x >= w)
return res >= K
ok = 10 ** 19
ng = 0
while ok - ng > 1:
m = (ok + ng) // 2
if check(m): ok = m
else: ng = m
print(ok)
```
| 84,881 |
Provide a correct Python 3 solution for this coding contest problem.
In your garden, there is a long and narrow flowerbed that stretches infinitely to the east. You have decided to plant N kinds of flowers in this empty flowerbed. For convenience, we will call these N kinds of flowers Flower 1, 2, …, N. Also, we will call the position that is p centimeters from the west end of the flowerbed Position p.
You will plant Flower i (1 ≤ i ≤ N) as follows: first, plant one at Position w_i, then plant one every d_i centimeters endlessly toward the east. That is, Flower i will be planted at the positions w_i, w_i + d_i, w_i + 2 d_i, … Note that more than one flower may be planted at the same position.
Find the position at which the K-th flower from the west is planted. If more than one flower is planted at the same position, they are counted individually.
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ K ≤ 10^9
* 1 ≤ w_i ≤ 10^{18}
* 1 ≤ d_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
w_1 d_1
:
w_N d_N
Output
When the K-th flower from the west is planted at Position X, print the value of X. (The westmost flower is counted as the 1-st flower.)
Examples
Input
2 6
20 10
25 15
Output
50
Input
3 9
10 10
10 10
10 10
Output
30
Input
1 1000000000
1000000000000000000 1000000000
Output
1999999999000000000
"Correct Solution:
```
import sys
N, K = map(int, input().split())
input = sys.stdin.readline
wd = [tuple(map(int, input().split())) for i in range(N)]
wd.sort()
d = 0
dp = [0]*N
l = 0
r = wd[0][0] + wd[0][1]*K
while(r - l > 1):
tmp = (l+r)//2
num = 0
for w, d in wd:
if w <= tmp:
num += ((tmp - w) // d) + 1
if num >= K:
r = tmp
else:
l = tmp
print(r)
```
| 84,882 |
Provide a correct Python 3 solution for this coding contest problem.
In your garden, there is a long and narrow flowerbed that stretches infinitely to the east. You have decided to plant N kinds of flowers in this empty flowerbed. For convenience, we will call these N kinds of flowers Flower 1, 2, …, N. Also, we will call the position that is p centimeters from the west end of the flowerbed Position p.
You will plant Flower i (1 ≤ i ≤ N) as follows: first, plant one at Position w_i, then plant one every d_i centimeters endlessly toward the east. That is, Flower i will be planted at the positions w_i, w_i + d_i, w_i + 2 d_i, … Note that more than one flower may be planted at the same position.
Find the position at which the K-th flower from the west is planted. If more than one flower is planted at the same position, they are counted individually.
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ K ≤ 10^9
* 1 ≤ w_i ≤ 10^{18}
* 1 ≤ d_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
w_1 d_1
:
w_N d_N
Output
When the K-th flower from the west is planted at Position X, print the value of X. (The westmost flower is counted as the 1-st flower.)
Examples
Input
2 6
20 10
25 15
Output
50
Input
3 9
10 10
10 10
10 10
Output
30
Input
1 1000000000
1000000000000000000 1000000000
Output
1999999999000000000
"Correct Solution:
```
n,k=map(int,input().split())
a=[list(map(int,input().split()))for i in range(n)]
l,r=2*(10**18)+1,0
while l-r>1:
t=(l+r)//2
c=0
for i,j in a:
c+=max(0,(t-i)//j+1)
if c<k:
r=t
else:
l=t
print(l)
```
| 84,883 |
Provide a correct Python 3 solution for this coding contest problem.
In your garden, there is a long and narrow flowerbed that stretches infinitely to the east. You have decided to plant N kinds of flowers in this empty flowerbed. For convenience, we will call these N kinds of flowers Flower 1, 2, …, N. Also, we will call the position that is p centimeters from the west end of the flowerbed Position p.
You will plant Flower i (1 ≤ i ≤ N) as follows: first, plant one at Position w_i, then plant one every d_i centimeters endlessly toward the east. That is, Flower i will be planted at the positions w_i, w_i + d_i, w_i + 2 d_i, … Note that more than one flower may be planted at the same position.
Find the position at which the K-th flower from the west is planted. If more than one flower is planted at the same position, they are counted individually.
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ K ≤ 10^9
* 1 ≤ w_i ≤ 10^{18}
* 1 ≤ d_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
w_1 d_1
:
w_N d_N
Output
When the K-th flower from the west is planted at Position X, print the value of X. (The westmost flower is counted as the 1-st flower.)
Examples
Input
2 6
20 10
25 15
Output
50
Input
3 9
10 10
10 10
10 10
Output
30
Input
1 1000000000
1000000000000000000 1000000000
Output
1999999999000000000
"Correct Solution:
```
import sys
input=sys.stdin.readline
N,K=map(int,input().split())
L=[]
for i in range(N):
s,d=map(int,input().split())
L.append([s,d])
High=10**20
Low =0
while High - Low >1:
Mid=(High + Low)//2
cnt=0
for j in range(N):
if Mid-L[j][0]<0:
continue
else:
cnt+=max(0,1+(Mid - L[j][0])//L[j][1])
if cnt>=K:
High = Mid
else:
Low = Mid
#print(High , Low)
Mid=int(Mid)
ans=0
for j in range(N):
ans+=max(0,1+(Mid - L[j][0])//L[j][1])
if ans>=K:
print(Mid)
else:
print(Mid+1)
```
| 84,884 |
Provide a correct Python 3 solution for this coding contest problem.
In your garden, there is a long and narrow flowerbed that stretches infinitely to the east. You have decided to plant N kinds of flowers in this empty flowerbed. For convenience, we will call these N kinds of flowers Flower 1, 2, …, N. Also, we will call the position that is p centimeters from the west end of the flowerbed Position p.
You will plant Flower i (1 ≤ i ≤ N) as follows: first, plant one at Position w_i, then plant one every d_i centimeters endlessly toward the east. That is, Flower i will be planted at the positions w_i, w_i + d_i, w_i + 2 d_i, … Note that more than one flower may be planted at the same position.
Find the position at which the K-th flower from the west is planted. If more than one flower is planted at the same position, they are counted individually.
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ K ≤ 10^9
* 1 ≤ w_i ≤ 10^{18}
* 1 ≤ d_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
w_1 d_1
:
w_N d_N
Output
When the K-th flower from the west is planted at Position X, print the value of X. (The westmost flower is counted as the 1-st flower.)
Examples
Input
2 6
20 10
25 15
Output
50
Input
3 9
10 10
10 10
10 10
Output
30
Input
1 1000000000
1000000000000000000 1000000000
Output
1999999999000000000
"Correct Solution:
```
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
import bisect
import random
from itertools import permutations, accumulate, combinations
import sys
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor
INF = float('inf')
def LI(): return list(map(int, sys.stdin.readline().split()))
def I(): return int(sys.stdin.readline())
def LIM(): return list(map(lambda x:int(x) - 1, sys.stdin.readline().split()))
def LS(): return sys.stdin.readline().split()
def S(): return sys.stdin.readline().strip()
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def LIRM(n): return [LIM() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
mod = 1000000007
n, k = LI()
left = 0
right = 2 * 10 ** 18
L = LIR(n)
while left <= right:
mid = (left + right) // 2
flag = False
ret = 0
for w, d in L:
if w == mid:
ret += 1
elif w < mid:
ret += 1
ret += (mid - w) // d
if ret >= k:
flag = True
right = mid - 1
else:
flag = False
left = mid + 1
if flag:
print(mid)
else:
print(mid + 1)
```
| 84,885 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In your garden, there is a long and narrow flowerbed that stretches infinitely to the east. You have decided to plant N kinds of flowers in this empty flowerbed. For convenience, we will call these N kinds of flowers Flower 1, 2, …, N. Also, we will call the position that is p centimeters from the west end of the flowerbed Position p.
You will plant Flower i (1 ≤ i ≤ N) as follows: first, plant one at Position w_i, then plant one every d_i centimeters endlessly toward the east. That is, Flower i will be planted at the positions w_i, w_i + d_i, w_i + 2 d_i, … Note that more than one flower may be planted at the same position.
Find the position at which the K-th flower from the west is planted. If more than one flower is planted at the same position, they are counted individually.
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ K ≤ 10^9
* 1 ≤ w_i ≤ 10^{18}
* 1 ≤ d_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
w_1 d_1
:
w_N d_N
Output
When the K-th flower from the west is planted at Position X, print the value of X. (The westmost flower is counted as the 1-st flower.)
Examples
Input
2 6
20 10
25 15
Output
50
Input
3 9
10 10
10 10
10 10
Output
30
Input
1 1000000000
1000000000000000000 1000000000
Output
1999999999000000000
Submitted Solution:
```
import sys
sys.setrecursionlimit(10**8)
input = sys.stdin.readline
n, k = [int(item) for item in input().split()]
wd = []
for i in range(n):
w, d = [int(item) for item in input().split()]
wd.append((w, d))
l = -1; r = 10**20
while r - l > 1:
mid = (l + r) // 2
flower = 0
for w, d in wd:
if mid - w >= 0:
flower += (mid - w) // d + 1
if flower >= k:
break
if flower >= k:
r = mid
else:
l = mid
print(r)
```
Yes
| 84,886 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In your garden, there is a long and narrow flowerbed that stretches infinitely to the east. You have decided to plant N kinds of flowers in this empty flowerbed. For convenience, we will call these N kinds of flowers Flower 1, 2, …, N. Also, we will call the position that is p centimeters from the west end of the flowerbed Position p.
You will plant Flower i (1 ≤ i ≤ N) as follows: first, plant one at Position w_i, then plant one every d_i centimeters endlessly toward the east. That is, Flower i will be planted at the positions w_i, w_i + d_i, w_i + 2 d_i, … Note that more than one flower may be planted at the same position.
Find the position at which the K-th flower from the west is planted. If more than one flower is planted at the same position, they are counted individually.
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ K ≤ 10^9
* 1 ≤ w_i ≤ 10^{18}
* 1 ≤ d_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
w_1 d_1
:
w_N d_N
Output
When the K-th flower from the west is planted at Position X, print the value of X. (The westmost flower is counted as the 1-st flower.)
Examples
Input
2 6
20 10
25 15
Output
50
Input
3 9
10 10
10 10
10 10
Output
30
Input
1 1000000000
1000000000000000000 1000000000
Output
1999999999000000000
Submitted Solution:
```
def examA():
N = I()
T = LI()
A = LI()
S = [-1]*N
S[0] = T[0]; S[-1]=A[-1]
ans = 1
for i in range(1,N):
if T[i]==T[i-1]:
continue
S[i] = T[i]
flag = -1
for i in range(N):
if S[i]==A[i]:
flag = i
break
if not (A[flag]==A[0] and A[flag]==T[-1]):
print(0)
return
for i in range(N-1)[::-1]:
if A[i]==A[i+1]:
continue
if S[i]==-1:
S[i] = A[i]
else:
S[i] = max(S[i],A[i])
#print(S)
P = []
pindex = []
for i in range(N):
if S[i]==-1:
continue
P.append(S[i])
pindex.append(i)
flag_U = True
for i in range(len(P)-1):
if P[i+1]>P[i]:
if not flag_U:
print(0)
return
elif P[i+1]<P[i]:
flag_U = False
ans = 1
p = -1
for i in range(N):
if S[i]==-1:
cur = min(P[p + 1], P[p])
ans *= cur
ans %= mod
else:
p += 1
print(ans)
return
def examB():
T = I()
A = LI()
ans = 0
print(ans)
return
def examC():
def dfs(n,s,edges,visited):
cost = BC[s]
now = []
for i in edges[s]:
if visited[i]:
continue
visited[i] = True
cur,visited = dfs(n,i,edges,visited)
now.append((cur, i))
now.sort()
for c,i in now:
cost += c-now[0][0]
children[i] = c-now[0][0]
return cost,visited
N, M = LI()
V = [[]for _ in range(N)]
for i in range(N-1):
p = I()
V[i+1].append(p)
V[p].append(i+1)
children = [-1]*N
BC = defaultdict(int)
for i in range(M):
b, c = LI()
BC[b] = c
visited = [False]*N
visited[0] = True
ans = dfs(N,0,V,visited)
print(children)
print(ans)
return
def examD():
N, K = LI()
W = [LI()for _ in range(N)]
l = 0; r = 10**20
while(r-l>1):
now = (l+r)//2
cur = 0
for i in range(N):
if now>=W[i][0]:
cur += ((now-W[i][0])//W[i][1]+1)
if cur<K:
l = now
else:
r = now
ans = r
print(ans)
return
import sys,copy,bisect,itertools,heapq,math,random
from heapq import heappop,heappush,heapify
from collections import Counter,defaultdict,deque
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))
def LSI(): return list(map(str,sys.stdin.readline().split()))
def LS(): return sys.stdin.readline().split()
def SI(): return sys.stdin.readline().strip()
global mod,mod2,inf,alphabet,_ep
mod = 10**9 + 7
mod2 = 998244353
inf = 10**18
_ep = 10**(-12)
alphabet = [chr(ord('a') + i) for i in range(26)]
if __name__ == '__main__':
examD()
"""
"""
```
Yes
| 84,887 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In your garden, there is a long and narrow flowerbed that stretches infinitely to the east. You have decided to plant N kinds of flowers in this empty flowerbed. For convenience, we will call these N kinds of flowers Flower 1, 2, …, N. Also, we will call the position that is p centimeters from the west end of the flowerbed Position p.
You will plant Flower i (1 ≤ i ≤ N) as follows: first, plant one at Position w_i, then plant one every d_i centimeters endlessly toward the east. That is, Flower i will be planted at the positions w_i, w_i + d_i, w_i + 2 d_i, … Note that more than one flower may be planted at the same position.
Find the position at which the K-th flower from the west is planted. If more than one flower is planted at the same position, they are counted individually.
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ K ≤ 10^9
* 1 ≤ w_i ≤ 10^{18}
* 1 ≤ d_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
w_1 d_1
:
w_N d_N
Output
When the K-th flower from the west is planted at Position X, print the value of X. (The westmost flower is counted as the 1-st flower.)
Examples
Input
2 6
20 10
25 15
Output
50
Input
3 9
10 10
10 10
10 10
Output
30
Input
1 1000000000
1000000000000000000 1000000000
Output
1999999999000000000
Submitted Solution:
```
# Atcoder problem Solving
# Code Festival Team Relay
import math
N, K = map(int, input().split())
que = [tuple(map(int, input().split())) for _ in range(N)]
def count(X):
cnt = 0
for i in range(N):
w, d = que[i]
if X >= w:
cnt+=(X-w)//d+1
return cnt
# case_impossible
l = -1
# case_possible
r = 10**19
while r-l > 1:
m = (l+r)//2
if count(m) < K:
l = m
else:
r = m
print(r)
```
Yes
| 84,888 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In your garden, there is a long and narrow flowerbed that stretches infinitely to the east. You have decided to plant N kinds of flowers in this empty flowerbed. For convenience, we will call these N kinds of flowers Flower 1, 2, …, N. Also, we will call the position that is p centimeters from the west end of the flowerbed Position p.
You will plant Flower i (1 ≤ i ≤ N) as follows: first, plant one at Position w_i, then plant one every d_i centimeters endlessly toward the east. That is, Flower i will be planted at the positions w_i, w_i + d_i, w_i + 2 d_i, … Note that more than one flower may be planted at the same position.
Find the position at which the K-th flower from the west is planted. If more than one flower is planted at the same position, they are counted individually.
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ K ≤ 10^9
* 1 ≤ w_i ≤ 10^{18}
* 1 ≤ d_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
w_1 d_1
:
w_N d_N
Output
When the K-th flower from the west is planted at Position X, print the value of X. (The westmost flower is counted as the 1-st flower.)
Examples
Input
2 6
20 10
25 15
Output
50
Input
3 9
10 10
10 10
10 10
Output
30
Input
1 1000000000
1000000000000000000 1000000000
Output
1999999999000000000
Submitted Solution:
```
n, k = map(int, input().split())
kadan = [list(map(int, input().split())) for _ in range(n)]
left = 0
right = 10**18*2
while right -left > 1:
mid = (right+left)//2
cnt = 0
for i in range(n):
if mid >= kadan[i][0]:
cnt += (mid - kadan[i][0])//kadan[i][1] + 1
if k > cnt :
left = mid
elif k <= cnt :
right = mid
print(right)
```
Yes
| 84,889 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In your garden, there is a long and narrow flowerbed that stretches infinitely to the east. You have decided to plant N kinds of flowers in this empty flowerbed. For convenience, we will call these N kinds of flowers Flower 1, 2, …, N. Also, we will call the position that is p centimeters from the west end of the flowerbed Position p.
You will plant Flower i (1 ≤ i ≤ N) as follows: first, plant one at Position w_i, then plant one every d_i centimeters endlessly toward the east. That is, Flower i will be planted at the positions w_i, w_i + d_i, w_i + 2 d_i, … Note that more than one flower may be planted at the same position.
Find the position at which the K-th flower from the west is planted. If more than one flower is planted at the same position, they are counted individually.
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ K ≤ 10^9
* 1 ≤ w_i ≤ 10^{18}
* 1 ≤ d_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
w_1 d_1
:
w_N d_N
Output
When the K-th flower from the west is planted at Position X, print the value of X. (The westmost flower is counted as the 1-st flower.)
Examples
Input
2 6
20 10
25 15
Output
50
Input
3 9
10 10
10 10
10 10
Output
30
Input
1 1000000000
1000000000000000000 1000000000
Output
1999999999000000000
Submitted Solution:
```
def solve(l, r):
if l > r:
return l
m = (l + r) // 2
t = sum((m - w) // d + 1 for w, d in flowers)
if t < k:
l = m + 1
else:
r = m - 1
return solve(l, r)
n, k = map(int, input().split())
flowers = [tuple(map(int, input().split())) for _ in range(n)]
print(solve(1, flowers[0][0] + flowers[0][1] * k))
```
No
| 84,890 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In your garden, there is a long and narrow flowerbed that stretches infinitely to the east. You have decided to plant N kinds of flowers in this empty flowerbed. For convenience, we will call these N kinds of flowers Flower 1, 2, …, N. Also, we will call the position that is p centimeters from the west end of the flowerbed Position p.
You will plant Flower i (1 ≤ i ≤ N) as follows: first, plant one at Position w_i, then plant one every d_i centimeters endlessly toward the east. That is, Flower i will be planted at the positions w_i, w_i + d_i, w_i + 2 d_i, … Note that more than one flower may be planted at the same position.
Find the position at which the K-th flower from the west is planted. If more than one flower is planted at the same position, they are counted individually.
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ K ≤ 10^9
* 1 ≤ w_i ≤ 10^{18}
* 1 ≤ d_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
w_1 d_1
:
w_N d_N
Output
When the K-th flower from the west is planted at Position X, print the value of X. (The westmost flower is counted as the 1-st flower.)
Examples
Input
2 6
20 10
25 15
Output
50
Input
3 9
10 10
10 10
10 10
Output
30
Input
1 1000000000
1000000000000000000 1000000000
Output
1999999999000000000
Submitted Solution:
```
# Atcoder problem Solving
# Code Festival Team Relay
import math
N, K = map(int, input().split())
que = [tuple(map(int, input().split())) for _ in range(N)]
def count(X):
cnt = 0
for i in range(N):
w, d = que[i]
if X >= w:
cnt+=(X-w)//d+1
return cnt
# case_impossible
l = -1
# case_possible
r = 10**25
while r-l > 1:
m = (l+r)//2
if count(m) < K:
l = m
else:
r = m
print(r)
```
No
| 84,891 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In your garden, there is a long and narrow flowerbed that stretches infinitely to the east. You have decided to plant N kinds of flowers in this empty flowerbed. For convenience, we will call these N kinds of flowers Flower 1, 2, …, N. Also, we will call the position that is p centimeters from the west end of the flowerbed Position p.
You will plant Flower i (1 ≤ i ≤ N) as follows: first, plant one at Position w_i, then plant one every d_i centimeters endlessly toward the east. That is, Flower i will be planted at the positions w_i, w_i + d_i, w_i + 2 d_i, … Note that more than one flower may be planted at the same position.
Find the position at which the K-th flower from the west is planted. If more than one flower is planted at the same position, they are counted individually.
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ K ≤ 10^9
* 1 ≤ w_i ≤ 10^{18}
* 1 ≤ d_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
w_1 d_1
:
w_N d_N
Output
When the K-th flower from the west is planted at Position X, print the value of X. (The westmost flower is counted as the 1-st flower.)
Examples
Input
2 6
20 10
25 15
Output
50
Input
3 9
10 10
10 10
10 10
Output
30
Input
1 1000000000
1000000000000000000 1000000000
Output
1999999999000000000
Submitted Solution:
```
import sys
sys.setrecursionlimit(10**8)
input = sys.stdin.readline
n, k = [int(item) for item in input().split()]
wd = []
for i in range(n):
w, d = [int(item) for item in input().split()]
wd.append((w, d))
l = -1; r = 10**20
while r - l > 1:
mid = (l + r) // 2
flower = 0
for w, d in wd:
flower += (mid - w) // d + 1
if flower > k:
break
if flower >= k:
r = mid
else:
l = mid
print(r)
```
No
| 84,892 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In your garden, there is a long and narrow flowerbed that stretches infinitely to the east. You have decided to plant N kinds of flowers in this empty flowerbed. For convenience, we will call these N kinds of flowers Flower 1, 2, …, N. Also, we will call the position that is p centimeters from the west end of the flowerbed Position p.
You will plant Flower i (1 ≤ i ≤ N) as follows: first, plant one at Position w_i, then plant one every d_i centimeters endlessly toward the east. That is, Flower i will be planted at the positions w_i, w_i + d_i, w_i + 2 d_i, … Note that more than one flower may be planted at the same position.
Find the position at which the K-th flower from the west is planted. If more than one flower is planted at the same position, they are counted individually.
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ K ≤ 10^9
* 1 ≤ w_i ≤ 10^{18}
* 1 ≤ d_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
w_1 d_1
:
w_N d_N
Output
When the K-th flower from the west is planted at Position X, print the value of X. (The westmost flower is counted as the 1-st flower.)
Examples
Input
2 6
20 10
25 15
Output
50
Input
3 9
10 10
10 10
10 10
Output
30
Input
1 1000000000
1000000000000000000 1000000000
Output
1999999999000000000
Submitted Solution:
```
import math
n,k=map(int,input().split())
a=[list(map(int,input().split())) for _ in range(n)]
l,r=-1,10**19
while r-l>1:
m=(l+r)//2
b=0
for w,d in a:
b+=(m-w+d-1)//d
if b<k:
l=m
else:
r=m
print(r+1)
```
No
| 84,893 |
Provide a correct Python 3 solution for this coding contest problem.
There is a tree with N vertices numbered 1, 2, ..., N. The edges of the tree are denoted by (x_i, y_i).
On this tree, Alice and Bob play a game against each other. Starting from Alice, they alternately perform the following operation:
* Select an existing edge and remove it from the tree, disconnecting it into two separate connected components. Then, remove the component that does not contain Vertex 1.
A player loses the game when he/she is unable to perform the operation. Determine the winner of the game assuming that both players play optimally.
Constraints
* 2 \leq N \leq 100000
* 1 \leq x_i, y_i \leq N
* The given graph is a tree.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_{N-1} y_{N-1}
Output
Print `Alice` if Alice wins; print `Bob` if Bob wins.
Examples
Input
5
1 2
2 3
2 4
4 5
Output
Alice
Input
5
1 2
2 3
1 4
4 5
Output
Bob
Input
6
1 2
2 4
5 1
6 3
3 2
Output
Alice
Input
7
1 2
3 7
4 6
2 3
2 4
1 5
Output
Bob
"Correct Solution:
```
import sys
n = int(sys.stdin.buffer.readline())
mp = map(int, sys.stdin.buffer.read().split())
links = [set() for _ in range(n)]
for x, y in zip(mp, mp):
x -= 1
y -= 1
links[x].add(y)
links[y].add(x)
stack = [(0, -2)]
grundy = [0] * n
while stack:
v, p = stack.pop()
if p == -1:
g = 0
# second visit (aggregate children and calculate self grundy)
for u in links[v]:
g ^= grundy[u] + 1
grundy[v] = g
else:
# first visit (stack children and remove parent)
links[v].discard(p)
stack.append((v, -1))
for u in links[v]:
stack.append((u, v))
if grundy[0] == 0:
print('Bob')
else:
print('Alice')
```
| 84,894 |
Provide a correct Python 3 solution for this coding contest problem.
There is a tree with N vertices numbered 1, 2, ..., N. The edges of the tree are denoted by (x_i, y_i).
On this tree, Alice and Bob play a game against each other. Starting from Alice, they alternately perform the following operation:
* Select an existing edge and remove it from the tree, disconnecting it into two separate connected components. Then, remove the component that does not contain Vertex 1.
A player loses the game when he/she is unable to perform the operation. Determine the winner of the game assuming that both players play optimally.
Constraints
* 2 \leq N \leq 100000
* 1 \leq x_i, y_i \leq N
* The given graph is a tree.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_{N-1} y_{N-1}
Output
Print `Alice` if Alice wins; print `Bob` if Bob wins.
Examples
Input
5
1 2
2 3
2 4
4 5
Output
Alice
Input
5
1 2
2 3
1 4
4 5
Output
Bob
Input
6
1 2
2 4
5 1
6 3
3 2
Output
Alice
Input
7
1 2
3 7
4 6
2 3
2 4
1 5
Output
Bob
"Correct Solution:
```
class Tree():
def __init__(self, n, decrement=1):
self.n = n
self.edges = [[] for _ in range(n)]
self.root = None
self.depth = [-1]*n
self.size = [1]*n # 部分木のノードの数
self.decrement = decrement
def add_edge(self, u, v):
u, v = u-self.decrement, v-self.decrement
self.edges[u].append(v)
self.edges[v].append(u)
def add_edges(self, edges):
for u, v in edges:
u, v = u-self.decrement, v-self.decrement
self.edges[u].append(v)
self.edges[v].append(u)
def set_root(self, root):
root -= self.decrement
self.root = root
self.par = [-1]*self.n
self.depth[root] = 0
self.order = [root] # 帰りがけに使う
next_set = [root]
while next_set:
p = next_set.pop()
for q in self.edges[p]:
if self.depth[q] != -1: continue
self.par[q] = p
self.depth[q] = self.depth[p]+1
self.order.append(q)
next_set.append(q)
for p in self.order[::-1]:
for q in self.edges[p]:
if self.par[p] == q: continue
self.size[p] += self.size[q]
#########################################################################################################
import sys
input = sys.stdin.readline
N = int(input())
T = Tree(N, decrement=1)
for _ in range(N-1):
x, y = map(int, input().split())
T.add_edge(x, y)
T.set_root(1)
grundy = [0]*N
for p in T.order[::-1]:
for q in T.edges[p]:
if T.par[p]==q: continue
grundy[p]^=grundy[q]+1
print("Alice" if grundy[0]!=0 else "Bob")
```
| 84,895 |
Provide a correct Python 3 solution for this coding contest problem.
There is a tree with N vertices numbered 1, 2, ..., N. The edges of the tree are denoted by (x_i, y_i).
On this tree, Alice and Bob play a game against each other. Starting from Alice, they alternately perform the following operation:
* Select an existing edge and remove it from the tree, disconnecting it into two separate connected components. Then, remove the component that does not contain Vertex 1.
A player loses the game when he/she is unable to perform the operation. Determine the winner of the game assuming that both players play optimally.
Constraints
* 2 \leq N \leq 100000
* 1 \leq x_i, y_i \leq N
* The given graph is a tree.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_{N-1} y_{N-1}
Output
Print `Alice` if Alice wins; print `Bob` if Bob wins.
Examples
Input
5
1 2
2 3
2 4
4 5
Output
Alice
Input
5
1 2
2 3
1 4
4 5
Output
Bob
Input
6
1 2
2 4
5 1
6 3
3 2
Output
Alice
Input
7
1 2
3 7
4 6
2 3
2 4
1 5
Output
Bob
"Correct Solution:
```
#!usr/bin/env python3
from collections import defaultdict, deque
from heapq import heappush, heappop
from itertools import permutations, accumulate
import sys
import math
import bisect
def LI(): return [int(x) for x in sys.stdin.buffer.readline().split()]
def I(): return int(sys.stdin.buffer.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
res = list(sys.stdin.readline())
if res[-1] == "\n":
return res[:-1]
return res
def IR(n):
return [I() for i in range(n)]
def LIR(n):
return [LI() for i in range(n)]
def SR(n):
return [S() for i in range(n)]
def LSR(n):
return [LS() for i in range(n)]
sys.setrecursionlimit(1000000)
mod = 1000000007
def solve():
n = I()
v = [[] for i in range(n)]
for i in range(n-1):
a,b = LI()
a -= 1
b -= 1
v[a].append(b)
v[b].append(a)
q = [0]
q2 = []
g = [0]*n
bfs = [1]*n
bfs[0] = 0
d = [0]*n
while q:
x = q.pop()
for y in v[x]:
if bfs[y]:
bfs[y] = 0
d[x] += 1
q.append(y)
q2.append((x,y))
while q2:
x,y = q2.pop()
g[x] ^= g[y]+1
ans = g[0]
if ans:
print("Alice")
else:
print("Bob")
return
#Solve
if __name__ == "__main__":
solve()
```
| 84,896 |
Provide a correct Python 3 solution for this coding contest problem.
There is a tree with N vertices numbered 1, 2, ..., N. The edges of the tree are denoted by (x_i, y_i).
On this tree, Alice and Bob play a game against each other. Starting from Alice, they alternately perform the following operation:
* Select an existing edge and remove it from the tree, disconnecting it into two separate connected components. Then, remove the component that does not contain Vertex 1.
A player loses the game when he/she is unable to perform the operation. Determine the winner of the game assuming that both players play optimally.
Constraints
* 2 \leq N \leq 100000
* 1 \leq x_i, y_i \leq N
* The given graph is a tree.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_{N-1} y_{N-1}
Output
Print `Alice` if Alice wins; print `Bob` if Bob wins.
Examples
Input
5
1 2
2 3
2 4
4 5
Output
Alice
Input
5
1 2
2 3
1 4
4 5
Output
Bob
Input
6
1 2
2 4
5 1
6 3
3 2
Output
Alice
Input
7
1 2
3 7
4 6
2 3
2 4
1 5
Output
Bob
"Correct Solution:
```
import sys
sys.setrecursionlimit(9**9)
n=int(input())
T=[[]for _ in"_"*(n+1)]
for _ in range(n-1):a,b=map(int,input().split());T[a]+=b,;T[b]+=a,
def d(v,p):
r=0
for s in T[v]:
if s!=p:r^=d(s,v)+1
return r
print("ABloibc e"[d(1,1)<1::2])
```
| 84,897 |
Provide a correct Python 3 solution for this coding contest problem.
There is a tree with N vertices numbered 1, 2, ..., N. The edges of the tree are denoted by (x_i, y_i).
On this tree, Alice and Bob play a game against each other. Starting from Alice, they alternately perform the following operation:
* Select an existing edge and remove it from the tree, disconnecting it into two separate connected components. Then, remove the component that does not contain Vertex 1.
A player loses the game when he/she is unable to perform the operation. Determine the winner of the game assuming that both players play optimally.
Constraints
* 2 \leq N \leq 100000
* 1 \leq x_i, y_i \leq N
* The given graph is a tree.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_{N-1} y_{N-1}
Output
Print `Alice` if Alice wins; print `Bob` if Bob wins.
Examples
Input
5
1 2
2 3
2 4
4 5
Output
Alice
Input
5
1 2
2 3
1 4
4 5
Output
Bob
Input
6
1 2
2 4
5 1
6 3
3 2
Output
Alice
Input
7
1 2
3 7
4 6
2 3
2 4
1 5
Output
Bob
"Correct Solution:
```
import sys
sys.setrecursionlimit(10**6)
n = int(input())
adj = [[] for _ in range(n)]
for _ in range(n-1):
x, y = map(int, input().split())
adj[x-1].append(y-1)
adj[y-1].append(x-1)
visited = [False for _ in range(n)]
def dfs(x):
global visited
nim = 0
for v in adj[x]:
if visited[v] == False:
visited[v] = True
nim ^= dfs(v)+1
return nim
visited[0] = True
if dfs(0) == 0:
print("Bob")
else:
print("Alice")
```
| 84,898 |
Provide a correct Python 3 solution for this coding contest problem.
There is a tree with N vertices numbered 1, 2, ..., N. The edges of the tree are denoted by (x_i, y_i).
On this tree, Alice and Bob play a game against each other. Starting from Alice, they alternately perform the following operation:
* Select an existing edge and remove it from the tree, disconnecting it into two separate connected components. Then, remove the component that does not contain Vertex 1.
A player loses the game when he/she is unable to perform the operation. Determine the winner of the game assuming that both players play optimally.
Constraints
* 2 \leq N \leq 100000
* 1 \leq x_i, y_i \leq N
* The given graph is a tree.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_{N-1} y_{N-1}
Output
Print `Alice` if Alice wins; print `Bob` if Bob wins.
Examples
Input
5
1 2
2 3
2 4
4 5
Output
Alice
Input
5
1 2
2 3
1 4
4 5
Output
Bob
Input
6
1 2
2 4
5 1
6 3
3 2
Output
Alice
Input
7
1 2
3 7
4 6
2 3
2 4
1 5
Output
Bob
"Correct Solution:
```
import sys
input = lambda: sys.stdin.readline().rstrip()
from collections import deque
N = int(input())
X = [[] for i in range(N)]
for i in range(N-1):
x, y = map(int, input().split())
X[x-1].append(y-1)
X[y-1].append(x-1)
P = [-1] * N
Q = deque([0])
R = []
while Q:
i = deque.popleft(Q)
R.append(i)
for a in X[i]:
if a != P[i]:
P[a] = i
X[a].remove(i)
deque.append(Q, a)
G = [0] * N
for i in R[::-1]:
s = 0
for j in X[i]:
s ^= G[j]
G[i] = s + 1
print("Bob" if G[0] == 1 else "Alice")
```
| 84,899 |
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