For a sequence S of positive integers and positive integers k and l, S is said to belong to level (k,l) when one of the following conditions is satisfied:

* The length of S is 1, and its only element is k.
* There exist sequences T_1,T_2,...,T_m (m \geq l) belonging to level (k-1,l) such that the concatenation of T_1,T_2,...,T_m in this order coincides with S.



Note that the second condition has no effect when k=1, that is, a sequence belongs to level (1,l) only if the first condition is satisfied.

Given are a sequence of positive integers A_1,A_2,...,A_N and a positive integer L. Find the number of subsequences A_i,A_{i+1},...,A_j (1 \leq i \leq j \leq N) that satisfy the following condition:

* There exists a positive integer K such that the sequence A_i,A_{i+1},...,A_j belongs to level (K,L).

Constraints

* 1 \leq N \leq 2 \times 10^5
* 2 \leq L \leq N
* 1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:


N L
A_1 A_2 ... A_N


Output

Print the number of subsequences A_i,A_{i+1},...,A_j (1 \leq i \leq j \leq N) that satisfy the condition.

Examples

Input

9 3
2 1 1 1 1 1 1 2 3


Output

22


Input

9 2
2 1 1 1 1 1 1 2 3


Output

41


Input

15 3
4 3 2 1 1 1 2 3 2 2 1 1 1 2 2


Output

31
// #pragma GCC target("avx")  // CPU 処理並列化
// #pragma GCC optimize("O3")  // CPU 処理並列化
// #pragma GCC optimize("unroll-loops")  // 条件処理の呼び出しを減らす
// #define BEGIN_STACK_EXTEND(size) void * stack_extend_memory_ = malloc(size);void * stack_extend_origin_memory_;char * stack_extend_dummy_memory_ = (char*)alloca((1+(int)(((long long)stack_extend_memory_)&127))*16);*stack_extend_dummy_memory_ = 0;asm volatile("mov %%rsp, %%rbx\nmov %%rax, %%rsp":"=b"(stack_extend_origin_memory_):"a"((char*)stack_extend_memory_+(size)-1024));
// #define END_STACK_EXTEND asm volatile("mov %%rax, %%rsp"::"a"(stack_extend_origin_memory_));free(stack_extend_memory_);

#include<stdio.h>
#include<math.h>
#include<algorithm>
#include<queue>
#include<deque>
#include<stack>
#include<string>
#include<string.h>
#include<vector>
#include<set>
#include<map>
#include<bitset>
#include<stdlib.h>
#include<cassert>
#include<time.h>
#include<bitset>
#include<numeric>
#include<unordered_set>
#include<unordered_map>
#include<complex>
using namespace std;
const long long mod=1000100000;
const long long inf=mod*mod;
const long long d2=(mod+1)/2;
const double EPS=1e-11;
const double INF=1e+10;
const double PI=acos(-1.0);
const int C_SIZE = 3100000;
const int UF_SIZE = 3100000;
namespace{
	long long fact[C_SIZE];
	long long finv[C_SIZE];
	long long inv[C_SIZE];
	inline long long Comb(int a,int b){
	 	if(a<b||b<0)return 0;
	 	return fact[a]*finv[b]%mod*finv[a-b]%mod;
	}
	void init_C(int n){
		fact[0]=finv[0]=inv[1]=1;
		for(int i=2;i<n;i++){
			inv[i]=(mod-(mod/i)*inv[mod%i]%mod)%mod;
		}
		for(int i=1;i<n;i++){
			fact[i]=fact[i-1]*i%mod;
			finv[i]=finv[i-1]*inv[i]%mod;
		}
	}
	long long pw(long long a,long long b){
		if(a<0LL)return 0;
		if(b<0LL)return 0;
		long long ret=1;
		while(b){
			if(b%2)ret=ret*a%mod;
			a=a*a%mod;
			b/=2;
		}
		return ret;
	}
	long long pw_mod(long long a,long long b,long long M){
		if(a<0LL)return 0;
		if(b<0LL)return 0;
		long long ret=1;
		while(b){
			if(b%2)ret=ret*a%M;
			a=a*a%M;
			b/=2;
		}
		return ret;
	}
	int pw_mod_int(int a,int b,int M){
		if(a<0)return 0;
		if(b<0)return 0;
		int ret=1;
		while(b){
			if(b%2)ret=(long long)ret*a%M;
			a=(long long)a*a%M;
			b/=2;
		}
		return ret;
	}
	int ABS(int a){return max(a,-a);}
	long long ABS(long long a){return max(a,-a);}
	double ABS(double a){return max(a,-a);}
	int sig(double r) { return (r < -EPS) ? -1 : (r > +EPS) ? +1 : 0; }
	int UF[UF_SIZE];
	void init_UF(int n){
		for(int i=0;i<n;i++)UF[i]=-1;
	}
	int FIND(int a){
		if(UF[a]<0)return a;
		return UF[a]=FIND(UF[a]);
	}
	void UNION(int a,int b){
		a=FIND(a);b=FIND(b);if(a==b)return;
		if(UF[a]>UF[b])swap(a,b);
		UF[a]+=UF[b];UF[b]=a;
	}
}
// ここから編集しろ
int p[210000];
set<pair<int,int> > S;
set<pair<int,int> > T;
int L[210000];
int R[210000];
int C[210000];
int main(){
	int a,b;scanf("%d%d",&a,&b);
	for(int i=0;i<a;i++){
		scanf("%d",p+i);
	}
	for(int i=0;i<a;i++){
		L[i]=R[i]=1;
	}
	for(int i=0;i<a;i++){
		S.insert(make_pair(i,p[i]));
		T.insert(make_pair(p[i],i));
	}
	long long ret=0;
	while(1){
		pair<int,int> d=*(T.begin());
		if(d.first>=mod)break;
		vector<int>v;
		set<pair<int,int> >::iterator it=S.lower_bound(make_pair(d.second,d.first));
		while(it!=S.end()&&it->second==d.first){
			v.push_back(it->first);
			it++;
		}
		int cur=0;
		for(int i=0;i<v.size();i++){
			ret+=(long long)L[v[i]]*R[v[i]];
			if(i-b+1>=0){
				cur+=L[v[i-b+1]];
			}
			ret+=(long long)cur*R[v[i]];
		}
		vector<pair<pair<int,int>,pair<int,int> > >ad;
		if(v.size()<b){
			ad.push_back(make_pair(make_pair(d.second,mod),make_pair(0,0)));
		}else{
			for(int i=0;i<v.size()/b;i++){
				ad.push_back(make_pair(make_pair(d.second+i,d.first+1),make_pair(0,0)));
			}
			int s=v.size();

			for(int i=0;i<v.size();i++){
				int lv=L[v[i]];
				int rv=R[v[i]];
				if(v.size()/b-(v.size()-i)/b<ad.size())ad[v.size()/b-(v.size()-i)/b].second.first+=lv;
				if(i>=b-1)ad[(i-b+1)/b].second.second+=rv;
			}
			cur=0;
			for(int i=0;i<ad.size();i++){
				ret-=(long long)ad[i].second.first*ad[i].second.second;
				if(i-b+1>=0){
					cur+=ad[i-b+1].second.first;
				}
				ret-=(long long)cur*ad[i].second.second;
			}
		}
		for(int i=0;i<v.size();i++){
			S.erase(make_pair(v[i],d.first));
			T.erase(make_pair(d.first,v[i]));
		}
		for(int i=0;i<ad.size();i++){
			S.insert(ad[i].first);
			T.insert(make_pair(ad[i].first.second,ad[i].first.first));
			L[ad[i].first.first]=ad[i].second.first;
			R[ad[i].first.first]=ad[i].second.second;
		}
		// printf("%d %d: %lld\n",d.first,d.second,ret);
		// for(set<pair<int,int> >::iterator it=S.begin();it!=S.end();it++){
			// printf("%d %d %d %d\n",it->first,it->second,L[it->first],R[it->first]);
		// }
	}
	printf("%lld\n",ret);
}