problem

There are many $ N $ colored balls of different weights in the queue. The queue is in ascending order from the beginning: $ 1,2,3, \ dots, N-1, N, 1,2,3, \ dots, N-1, N, 1,2,3, \ dots $ The balls are lined up, followed by the balls of color $ N $, followed by the balls of color $ 1 $. Balls of the same color weigh the same, and balls of color $ i $ weigh $ A_i $.

From this state, take out $ M $ of balls from the beginning of the queue and repeat the process of grouping them. Then stop forming groups when the total number of balls of each color removed from the cue is equal. Please note that the cue contains a sufficient number of balls and the cue will not be empty by the time you stop forming groups.

For example, when $ N = 8, M = 2 $, there are 4 groups of {color 1, color 2}, {color 3, color 4}, {color 5, color 6}, {color 7, color 8}. (At this time, there is one ball of each color). When $ N = 4, M = 3 $, {color 1, color 2, color 3}, {color 4, color 1, color 2}, {color 3, color 4, color 1}, {color 2, color There will be a $ 4 $ group of 3, colors 4} (there are 3 balls of each color each).

At this time, in each group, the difference between the maximum value and the minimum value of the weight of the balls included is called the weight range of that group. Output the sum of the weight ranges for each group.



output

Print the answer in one line. Also, output a line break at the end.

Example

Input

8 2
23 61 57 13 91 41 79 41


Output

170
// need
#include <iostream>
#include <algorithm>

// data structure
#include <bitset>
//#include <list>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
//#include <array>
//#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <complex>
//#include <deque>
#include<valarray>

// stream
//#include <istream>
//#include <sstream>
//#include <ostream>

// etc
#include <cassert>
#include <functional>
#include <iomanip>
//#include <typeinfo>
#include <chrono>
#include <random>
#include <numeric>

#define INIT std::ios::sync_with_stdio(false);std::cin.tie(0);
#define VAR(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__);
template<typename T> void MACRO_VAR_Scan(T& t) { std::cin >> t; }
template<typename First, typename...Rest>void MACRO_VAR_Scan(First& first, Rest&...rest) { std::cin >> first; MACRO_VAR_Scan(rest...); }
#define VEC_ROW(type, n, ...)std::vector<type> __VA_ARGS__;MACRO_VEC_ROW_Init(n, __VA_ARGS__); for(int i=0; i<n; ++i){MACRO_VEC_ROW_Scan(i, __VA_ARGS__);}
template<typename T> void MACRO_VEC_ROW_Init(int n, T& t) { t.resize(n); }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Init(int n, First& first, Rest&...rest) { first.resize(n); MACRO_VEC_ROW_Init(n, rest...); }
template<typename T> void MACRO_VEC_ROW_Scan(int p, T& t) { std::cin >> t[p]; }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Scan(int p, First& first, Rest&...rest) { std::cin >> first[p]; MACRO_VEC_ROW_Scan(p, rest...); }
#define OUT(d) std::cout<<d;
#define FOUT(n, d) std::cout<<std::fixed<<std::setprecision(n)<<d;
#define SOUT(n, c, d) std::cout<<std::setw(n)<<std::setfill(c)<<d;
#define SP std::cout<<" ";
#define TAB std::cout<<"\t";
#define BR std::cout<<"\n";
#define ENDL std::cout<<std::endl;
#define FLUSH std::cout<<std::flush;
#define VEC(type, c, n) std::vector<type> c(n);for(auto& i:c)std::cin>>i;
#define MAT(type, c, m, n) std::vector<std::vector<type>> c(m, std::vector<type>(n));for(auto& r:c)for(auto& i:r)std::cin>>i;
#define ALL(a) (a).begin(),(a).end()
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define RFOR(i, a, b) for(int i=(b)-1;i>=(a);--i)
#define REP(i, n) for(int i=0;i<int(n);++i)
#define RREP(i, n) for(int i=(n)-1;i>=0;--i)
#define FORLL(i, a, b) for(ll i=ll(a);i<ll(b);++i)
#define RFORLL(i, a, b) for(ll i=ll(b)-1;i>=ll(a);--i)
#define REPLL(i, n) for(ll i=0;i<ll(n);++i)
#define RREPLL(i, n) for(ll i=ll(n)-1;i>=0;--i)
#define PAIR std::pair<int, int>
#define PAIRLL std::pair<ll, ll>
#define IN(a, x, b) (a<=x && x<b)
#define SHOW(d) {std::cerr << #d << "\t:" << d << "\n";}
#define SHOWVECTOR(v) {std::cerr << #v << "\t:";for(const auto& xxx : v){std::cerr << xxx << " ";}std::cerr << "\n";}
#define SHOWVECTOR2(v) {std::cerr << #v << "\t:\n";for(const auto& xxx : v){for(const auto& yyy : xxx){std::cerr << yyy << " ";}std::cerr << "\n";}}
#define SHOWPAIR(p) {std::cerr << #p << "\t:(" << p.first << ",\t" << p.second << ")\n";}
#define SHOWPAIRVECTOR2(v) {std::cerr << #v << "\t:\n";for(const auto& xxx : v){for(const auto& yyy : xxx){std::cerr<<'('<<yyy.first<<", "<<yyy.second<<") ";}std::cerr << "\n";}}
#define SHOWPAIRVECTOR(v) {for(const auto& xxx:v){std::cerr<<'('<<xxx.first<<", "<<xxx.second<<") ";}std::cerr<<"\n";}
#define SHOWQUEUE(a) {std::queue<decltype(a.front())> tmp(a);std::cerr << #a << "\t:";for(int i=0; i<static_cast<int>(a.size()); ++i){std::cerr << tmp.front() << "\n";tmp.pop();}std::cerr << "\n";}
template<typename T> inline T CHMAX(T& a, const T b) { return a = (a < b) ? b : a; }
template<typename T> inline T CHMIN(T& a, const T b) { return a = (a > b) ? b : a; }
#define EXCEPTION(msg) throw std::string("Exception : " msg " [ in ") + __func__ + " : " + std::to_string(__LINE__) + " lines ]"
#define TRY(cond, msg) try {if (cond) EXCEPTION(msg);}catch (std::string s) {std::cerr << s << std::endl;}
void CHECKTIME(std::function<void()> f) { auto start = std::chrono::system_clock::now(); f(); auto end = std::chrono::system_clock::now(); auto res = std::chrono::duration_cast<std::chrono::nanoseconds>((end - start)).count(); std::cerr << "[Time:" << res << "ns  (" << res / (1.0e9) << "s)]\n"; }

#define int ll
using ll = long long;
using ull = unsigned long long;
constexpr int INFINT = 1 << 30;                          // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;              // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                          // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62);  // 9.22x10^18
constexpr double EPS = 1e-7;
constexpr int MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;

//SegmentTree(?????°??¨)
template <class T>
class SegmentTree {
private:
	T init_val;
	std::vector<T> ary;
	std::function<T(T, T)> func;
public:
	// ?????¨???(??????????????§??????N??¨??????)
	// SegmentTree<T> st(N,  INF, [](T l, T r){return std::min(l, r);}); ????°????
	// SegmentTree<T> st(N, -INF, [](T l, T r){return std::max(l, r);}); ?????§???
	// SegmentTree<T> st(N,    0, [](T l, T r){return l+r;});            ????¨?
	SegmentTree(int n, T val, std::function<T(T, T)> f) : init_val(val), func(f) {
		ary.resize(static_cast<int>(std::pow(2, std::ceil(std::log(n) / std::log(2)) + 1) - 1), val);
	}
	void init(int n, T val, std::function<T(T, T)> f) {
		ary.resize(static_cast<int>(std::pow(2, std::ceil(1.0*std::log(n) / std::log(2)) + 1) - 1), val);
		init_val = val;
		func = f;
	}
	void update(int i, T val) {
		i += ary.size() / 2;
		ary[i] = val;
		while (i > 0) {
			i = (i - 1) / 2;
			ary[i] = func(ary[2 * i + 1], ary[2 * i + 2]);
		}
	}
	// ??????[a, b)???func????????????????????? (query_(a, b, 0, 0, n)??¨????????????)
	T query_(int a, int b, int i, int l, int r) {
		if (r <= a || b <= l) return init_val;
		if (a <= l && r <= b) return ary[i];
		else {
			T vl = query_(a, b, 2 * i + 1, l, (l + r) / 2);
			T vr = query_(a, b, 2 * i + 2, (l + r) / 2, r);
			return func(vl, vr);
		}
	}
	// ??????(b)????°??????§?????????????????????
	T query(int a, int b) {
		return query_(a, b, 0, 0, ary.size() / 2 + 1);
	}
};

ll gcd(ll a, ll b) {
	return b ? gcd(b, a%b) : a;
}

signed main() {
	INIT;
	VAR(int, n, m);
	VEC(int, a, n);
	a.insert(a.end(), ALL(a));
	SegmentTree<int> stmin(2*n, INFINT, [](int l, int r) {return std::min(l, r); });
	SegmentTree<int> stmax(2*n, -INFINT, [](int l, int r){return std::max(l, r);});
	REP(i, 2 * n) {
		stmin.update(i, a[i]);
		stmax.update(i, a[i]);
	}
	int g = gcd(n, m);
	int k = n / g;
	int ans = 0;
	for (int i = 0; k--; i += m) {
		int p = i%n;
		ans += stmax.query(p, p + m) - stmin.query(p, p + m);
	}
	OUT(ans)BR;
	return 0;
}