m, k = map(int, input().split())
A = list(map(int, input().split()))

ans = 0
cnt = [0] * m
left = 0
right = 0
plus = [0] * m
mi_cnt = [0] * m
pm = [0] * m
for i, a in enumerate(A):
    c = cnt[a] * m + a
    ans += abs(c - i)
    cnt[a] += 1
    if i <= c:
        left += 1
    else:
        right += 1
        
    l = c // m * m
    r = (c + m) // m * m
    if i <= l:
        plus[a] -= m
    elif i >= r:
        plus[a] += m
    else:
        mi_cnt[a] += 1
        plus[a] += (i - l) - (r - i)
        tmp = (i - a) % m
        pm[tmp] += 1

tot = ans
for i in range(1, m):
    tot += left - right + plus[m - i]
    left += -mi_cnt[m - i] + pm[i]
    right += mi_cnt[m - i] - pm[i]
    ans = min(ans, tot)
    
print(ans // 2)