Problem: Bob got a job as a system administrator in X corporation. His first task was to connect n servers with the help of m two-way direct connection so that it becomes possible to transmit data from one server to any other server via these connections. Each direct connection has to link two different servers, each pair of servers should have at most one direct connection. Y corporation, a business rival of X corporation, made Bob an offer that he couldn't refuse: Bob was asked to connect the servers in such a way, that when server with index v fails, the transmission of data between some other two servers becomes impossible, i.e. the system stops being connected. Help Bob connect the servers.

Input

The first input line contains 3 space-separated integer numbers n, m, v (3 ≤ n ≤ 105, 0 ≤ m ≤ 105, 1 ≤ v ≤ n), n — amount of servers, m — amount of direct connections, v — index of the server that fails and leads to the failure of the whole system.

Output

If it is impossible to connect the servers in the required way, output -1. Otherwise output m lines with 2 numbers each — description of all the direct connections in the system. Each direct connection is described by two numbers — indexes of two servers, linked by this direct connection. The servers are numbered from 1. If the answer is not unique, output any.

Examples

Input

5 6 3


Output

1 2
2 3
3 4
4 5
1 3
3 5


Input

6 100 1


Output

-1

Solution (in PYTHON3):

Solution:
#! /usr/bin/python3
# SUBMISSION 1 (wrong answer on test 1): big dumb forgot to print answer
# SUBMISSION 2 (runtime error on test 2): big dumb again forget to handle if m out of bounds
# SUBMISSION 3 (TLE on test 10): need to optimize, maybe change handling of calculating factorial? SOLUTION: tried eliminating factorial calculation
import sys
import math
import copy

big = set()
small = []

def main():
    input_list = get_input()
    line = [int(x) for x in input_list[0].split(" ")]
    solution = solve(line[0], line[1], line[2])
    if solution != -1:
        for i in solution:
            print(i)
    else:
        print(-1)

def get_input():
    input_list = []
    for line in sys.stdin:
        input_list.append(line.rstrip("\n"))
    return input_list

def generate_sets(n, m, v):
    global big
    global small

    if v == 1:
        small = [2, 1]
        for i in range(1, n + 1):
            big.add(i)
        big.remove(2)
        big = list(big)
    else:
        small = [1, v]
        for i in range(1, n + 1):
            big.add(i)
        big.remove(1)
        big = list(big)

    return None

def generate_basic_network(n, m, v):
    global big
    global small
    edges = set()
    
    temp = copy.deepcopy(big)
    temp = set(temp)
    temp.remove(v)
    temp = list(temp)
    basic = small + temp

    for i in range(len(basic) - 1):
        edges.add(str(basic[i]) + " " + str(basic[i + 1]))
    return edges

def solve(n, m, v):
    global big
    global small
    big = set()
    small = []
    edges = set()

    # m_max = 1 + (math.factorial(n - 1) / (2 * math.factorial(n - 3)))
    m_min = n - 1
    if m >= m_min:
        generate_sets(n, m, v)
        edges = generate_basic_network(n, m, v)
        for j in range(len(big)):
            if len(edges) == m:
                break
            for k in range(len(big[j + 1:])):
                if len(edges) == m:
                    break
                edge = str(big[j]) + " " + str(big[j + 1:][k])
                reverse_edge = str(big[j + 1:][k]) + " " + str(big[j])
                if not edge in edges and not reverse_edge in edges:
                    edges.add(edge)
        if len(edges) != m:
            return -1
        return edges
    else:
        return -1

if __name__ == "__main__":
    main()