Problem

Given a permutation of length $ N $ $ P = \\ {P_1, P_2, \ ldots, P_N \\} $ and the integer $ K $.
Determine if the permutation $ P $ can be monotonically increased by repeating the following operation any number of times $ 0 $ or more.

* Choose the integer $ x \ (0 \ le x \ le N-K) $. Patrol right shift around $ P_ {x + 1}, \ ldots, P_ {x + K} $



However, the cyclic right shift of the subsequence $ U = U_1, \ ldots, U_M $ means that $ U = U_1, \ ldots, U_M $ is changed to $ U = U_M, U_1, \ ldots, U_ {M-1} $. Means to change.

Constraints

The input satisfies the following conditions.

* $ 2 \ leq K \ leq N \ leq 10 ^ 5 $
* $ 1 \ leq P_i \ leq N \ (1 \ leq i \ leq N) $
* $ P_i \ neq P_j \ (i \ neq j) $
* All inputs are integers

Input

The input is given in the following format.


$ N $ $ K $
$ P_1 $ $ \ ldots $ $ P_N $


Permutation length $ N $ and integer $ K $ are given in the first row, separated by blanks.
The elements of the permutation $ P $ are given in the second row, separated by blanks.

Output

Print "Yes" if you can monotonically increase $ P $, otherwise print "No" on the $ 1 $ line.

Examples

Input

3 3
2 3 1


Output

Yes


Input

3 2
1 2 3


Output

Yes


Input

3 3
3 2 1


Output

No
#include "bits/stdc++.h"

using namespace std;

//int N,M,K,L,R,H,W;
long long int N,M,K,L,R,H,W;

//constexpr long long int MOD=1000000007;
//constexpr  int MOD=1000000007;
constexpr int MOD=998244353;
//constexpr long long int MOD=998244353;

class Add_Segment_Tree {
	vector<long long int>v;
	vector<int>l;
	vector<int>r;
	long long int ret;
	int num;
	long long int Update(int place) {
		if (place >= v.size() / 2) {
			return v[place];
		}
		v[place] = Update(place * 2) + Update(place * 2 + 1);
		return v[place];
	}
	void Sum(int a, int b, int place) {
		if (l[place] >= a&&r[place] <= b) {
			ret += v[place];
			return;
		}
		if (l[place] > b || r[place] < a) return;
		Sum(a, b, place * 2);
		Sum(a, b, place * 2 + 1);
		return;
	}
public:
	void Left(int place) {
		if (place >= v.size() / 2) {
			l[place] = place - v.size() / 2;
			return;
		}
		Left(place * 2);
		Left(place * 2 + 1);
		l[place] = l[place * 2];
		return;
	}
	void Right(int place) {
		if (place >= v.size() / 2) {
			r[place] = place - v.size() / 2;
			return;
		}
		Right(place * 2);
		Right(place * 2 + 1);
		r[place] = r[place * 2 + 1];
		return;
	}
	Add_Segment_Tree(int n) {
		n++;
		num = 1;
		while (num < n * 2)num *= 2;
		l.resize(num);
		r.resize(num);
		v.resize(num, 0);
		Left(1);
		Right(1);
	}
	void Add(int place, long long int num, bool update) {
		place += v.size() / 2;
		v[place] += num;
		if (!update)return;
		place /= 2;
		while (place) {
			v[place] = v[place * 2] + v[place * 2 + 1];
			place /= 2;
		}
	}
	void TopDown() {
		Update(1);
	}
	long long int Sum(int a, int b) {
		ret = 0;
		Sum(a, b, 1);
		return ret;
	}
};

int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	
	cin>>N>>K;
	vector<int>v(N);
	for(auto &i:v)cin>>i;
	long long int box=0;
	Add_Segment_Tree asg(N+1);
	for(int i=0;i<N;i++){
		box+=asg.Sum(v[i],N);
		asg.Add(v[i],1,true);
	}
	if(box%2&&K%2){
		cout<<"No\n";
		return 0;
	}
	if(N==K){
		for(int i=0;i<N;i++){
			if((v[i]+1)%N!=(v[(i+1)%N])%N){
				cout<<"No\n";
				return 0;
			}
		}
	}
	cout<<"Yes\n";
	return 0;
}
