Problem:


Score : 300 points

Problem Statement

There is a circular pond with a perimeter of K meters, and N houses around them.

The i-th house is built at a distance of A_i meters from the northmost point of the pond, measured clockwise around the pond.

When traveling between these houses, you can only go around the pond.

Find the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.

Constraints

2 \leq K \leq 10^6

2 \leq N \leq 2 \times 10^5

0 \leq A_1 < ... < A_N < K

All values in input are integers.

Input

Input is given from Standard Input in the following format:

K N
A_1 A_2 ... A_N

Output

Print the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.

Sample Input 1

20 3
5 10 15

Sample Output 1

10

If you start at the 1-st house and go to the 2-nd and 3-rd houses in this order, the total distance traveled will be 10.

Sample Input 2

20 3
0 5 15

Sample Output 2

10

If you start at the 2-nd house and go to the 1-st and 3-rd houses in this order, the total distance traveled will be 10.



Sample input:
20 3
5 10 15


Sample output:
10

Submission status: Runtime Error

Solution code:
K,N=map(int,input().split())
A=list(map(int,input().split()))
A.sort()

def distance(x):
    q=x[1:]-x[:-1]
    return q

B=distance(A)
B.append(K+A[0]-A[N-1])
print(K-max(B))

Submission status: Runtime Error

Solution code:
k, n = map(int,input().split())
a = list(map(int,input().split()))

end = a[0] + k - a[n-1]
b = []
b.append(end)

for i in range(0,n-1):
    diff = a[i+1] - a[i]
    b.append(diff)

b.sort(reverse=True)
print(k-max)

Submission status: Runtime Error

Solution code:
20 3
0 5 15

Submission status: Runtime Error

Solution code:

from sys import stdin
import sys
sys.setrecursionlimit(10**8)

def getInputs():
	inputs=[]
	for line in stdin:
		line=line.split()
		inputs.append(line)
	return inputs

def main(inputs):
	k,n=getIntList(inputs[0])
	aList=getIntList(inputs[1])
	
	d=k-aList[n-1]+aList[0]
	di=n-1
# 	print(d,di)
	for ai in range(n-1):
		dd=aList[ai+1]-aList[ai]
# 		print(dd)
		if dd>d:
			di=ai
			d=dd
	
	print(k-d)


if __name__=="__main__":
	inputs=getInputs()
# 	inputs=simInputs()
	main(inputs)

Submission status: Runtime Error

Solution code:
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

def main():
    K, N = map(int, readline().split())
    A = map(int, readline().split())
    ans = max(K - max(A) + min(A),max(A) -min(A))
    print(ans)
    return

if __name__ == '__main__':
    main()

Submission status: Runtime Error

Solution code:
k, n = map(int, input().split())
A=[]
for i in range(n):
  A.append(int(input()))
B=[]
for i in range(n-1):
  B.append(A[i+1]-A[i])
B.append(k-A[n-1]+A[0])
print(k-max(B))

Submission status: Runtime Error

Solution code:
K, N = map(int, input().split())
A = list(map(int, input().split()))

m = K - A[N-1] + A[0]

for i in range(N):
  m = min(m, A[i+1] - A[i])

print(K - m)