You are given sequence a_1, a_2, ..., a_{n} and m queries l_{j}, r_{j} (1 ≤ l_{j} ≤ r_{j} ≤ n). For each query you need to print the minimum distance between such pair of elements a_{x} and a_{y} (x ≠ y), that:  both indexes of the elements lie within range [l_{j}, r_{j}], that is, l_{j} ≤ x, y ≤ r_{j};  the values of the elements are equal, that is a_{x} = a_{y}. 

The text above understands distance as |x - y|.


-----Input-----

The first line of the input contains a pair of integers n, m (1 ≤ n, m ≤ 5·10^5) — the length of the sequence and the number of queries, correspondingly. 

The second line contains the sequence of integers a_1, a_2, ..., a_{n} ( - 10^9 ≤ a_{i} ≤ 10^9). 

Next m lines contain the queries, one per line. Each query is given by a pair of numbers l_{j}, r_{j} (1 ≤ l_{j} ≤ r_{j} ≤ n) — the indexes of the query range limits.


-----Output-----

Print m integers — the answers to each query. If there is no valid match for some query, please print -1 as an answer to this query.


-----Examples-----
Input
5 3
1 1 2 3 2
1 5
2 4
3 5

Output
1
-1
2

Input
6 5
1 2 1 3 2 3
4 6
1 3
2 5
2 4
1 6

Output
2
2
3
-1
2

Difficulty: interview

Starter code:

Solutions:
import sys

class Fenwick(object):
  def __init__(self, n):
    self.n = n
    self.a = [10**9 for i in range(n)]
    self.w= 10**9

  def zag(self, i, zn):
    self.w= min(self.w, zn)
    while i < self.n:
      self.a[i] = min(self.a[i], zn)
      i = (i | (i + 1))

  def pol(self, r):
    ans= 10**9
    while r >= 0:
      if ans> self.a[r]:
        ans= self.a[r]
      if ans== self.w:
        break
      r = (r & (r + 1)) - 1
    return ans

n, m = [int(x) for x in sys.stdin.readline().split()]
a = [int(x) for x in sys.stdin.readline().split()]

nd= [-1 for i in range(0, len(a))]
vi= {}
for i in range(0, len(a)):
  if a[i] in vi:
    nd[i] = vi[a[i]]
  vi[a[i]] = i

inp= sys.stdin.readlines()
och= [[] for i in range(n)]
for i in range(m):
  l, r = inp[i].split()
  och[int(r) - 1].append((int(l) - 1, i))

der = Fenwick(2 ** 19)
ans= [None for i in range(0, m)]
le= -1
for r in range(n):
  if nd[r] != -1:
    der.zag(500000 - nd[r] + 1, r - nd[r])
    le = max(le, nd[r])
  for (l, ind) in och[r]:
    if l > le:
      ans[ind] = -1
      continue
    zn= der.pol(500000 - l + 1)
    if zn== 10**9:
      zn= -1
    ans[ind] = zn

print('\n'.join(str(zn) for zn in ans))

import sys

class Fenwick(object):
  def __init__(self, n):
    self.n = n
    self.a = [10**9 for i in range(n)]
    self.w= 10**9

  def zag(self, i, zn):
    self.w= min(self.w, zn)
    while i < self.n:
      self.a[i] = min(self.a[i], zn)
      i = (i | (i + 1))

  def pol(self, r):
    ans= 10**9
    while r >= 0:
      if ans> self.a[r]:
        ans= self.a[r]
      if ans== self.w:
        break
      r = (r & (r + 1)) - 1
    return ans

n, m = [int(x) for x in sys.stdin.readline().split()]
a = [int(x) for x in sys.stdin.readline().split()]

nd= [-1 for i in range(0, len(a))]
vi= {}
for i in range(0, len(a)):
  if a[i] in vi:
    nd[i] = vi[a[i]]
  vi[a[i]] = i

inp= sys.stdin.readlines()
och= [[] for i in range(n)]
for i in range(m):
  l, r = inp[i].split()
  och[int(r) - 1].append((int(l) - 1, i))

der = Fenwick(2 ** 19)
ans= [None for i in range(0, m)]
le= -1
for r in range(n):
  if nd[r] != -1:
    der.zag(500000 - nd[r] + 1, r - nd[r])
    le = max(le, nd[r])
  for (l, ind) in och[r]:
    if l > le:
      ans[ind] = -1
      continue
    zn= der.pol(500000 - l + 1)
    if zn== 10**9:
      zn= -1
    ans[ind] = zn

print('\n'.join(str(zn) for zn in ans))