Problem:
Score : 300 points

Problem Statement

In a public bath, there is a shower which emits water for T seconds when the switch is pushed.

If the switch is pushed when the shower is already emitting water, from that moment it will be emitting water for T seconds.
Note that it does not mean that the shower emits water for T additional seconds.

N people will push the switch while passing by the shower.
The i-th person will push the switch t_i seconds after the first person pushes it.

How long will the shower emit water in total?

Constraints

1 ≤ N ≤ 200,000

1 ≤ T ≤ 10^9

0 = t_1 < t_2 < t_3 < , ..., < t_{N-1} < t_N ≤ 10^9

T and each t_i are integers.

Input

Input is given from Standard Input in the following format:

N T
t_1 t_2 ... t_N

Output

Assume that the shower will emit water for a total of X seconds. Print X.

Sample Input 1

2 4
0 3

Sample Output 1

7

Three seconds after the first person pushes the water, the switch is pushed again and the shower emits water for four more seconds, for a total of seven seconds.

Sample Input 2

2 4
0 5

Sample Output 2

8

One second after the shower stops emission of water triggered by the first person, the switch is pushed again.

Sample Input 3

4 1000000000
0 1000 1000000 1000000000

Sample Output 3

2000000000

Sample Input 4

1 1
0

Sample Output 4

1

Sample Input 5

9 10
0 3 5 7 100 110 200 300 311

Sample Output 5

67

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#include<vector>
#include<map>
#include<set>
#include<algorithm>
#include<numeric>
#include<limits>
#include<bitset>
#include<functional>
#include<type_traits>

namespace lib
{
	template<std::uint64_t Mod>struct modnum;
	template<class T>constexpr T pow(T base, std::size_t p)
	{
		if (p == 0)
		{
			return T(1);
		}
		else if (p == 1)
		{
			return base;
		}
		else if (p == 2)
		{
			return base*base;
		}
		else if (p % 2 == 0)
		{
			return pow(pow(base, p / 2), 2);
		}
		else
		{
			return pow(pow(base, p / 2), 2)*base;
		}
	}
	template<std::uint64_t Mod>constexpr auto inverse(modnum<Mod> const&);

	template<std::uint64_t Mod>struct modnum
	{
		static constexpr auto mod = Mod;
		std::uint64_t val;
		modnum() = default;
		constexpr modnum(std::uint64_t v) :val(v%Mod)
		{

		}

		constexpr modnum& operator+=(modnum const& v)
		{
			val += v.val;
			val %= mod;
			return *this;
		}
		constexpr modnum& operator-=(modnum const& v)
		{
			val += mod - v.val;
			val %= mod;
			return *this;
		}
		constexpr modnum& operator*=(modnum const& v)
		{
			val *= v.val;
			val %= mod;
			return *this;
		}
		constexpr modnum& operator/=(modnum const& v)
		{
			return operator*=(inverse(v));
		}
	};
	template<std::uint64_t Mod>constexpr auto operator+(modnum<Mod> lhs, modnum<Mod>const& rhs)
	{
		return lhs += rhs;
	}
	template<std::uint64_t Mod>constexpr auto operator+(modnum<Mod> lhs, int rhs)
	{
		return lhs += rhs;
	}
	template<std::uint64_t Mod>constexpr auto operator+(int lhs, modnum<Mod> rhs)
	{
		return rhs += lhs;
	}
	template<std::uint64_t Mod>constexpr auto operator-(modnum<Mod> lhs, modnum<Mod>const& rhs)
	{
		return lhs -= rhs;
	}
	template<std::uint64_t Mod>constexpr auto operator*(modnum<Mod> lhs, modnum<Mod>const& rhs)
	{
		return lhs *= rhs;
	}
	template<std::uint64_t Mod>constexpr auto operator*(modnum<Mod> lhs, int rhs)
	{
		return lhs *= rhs;
	}
	template<std::uint64_t Mod>constexpr auto operator*(int lhs, modnum<Mod> rhs)
	{
		return rhs *= lhs;
	}

	template<std::uint64_t Mod>constexpr auto operator/(modnum<Mod> lhs, modnum<Mod>const& rhs)
	{
		return lhs /= rhs;
	}

	template<std::uint64_t Mod>constexpr auto inverse(modnum<Mod>const& base)
	{
		return pow(base, Mod - 2);
	}

	template<class T>constexpr auto clamp(T v)
	{
		return std::max(v, T());
	}
	template<class T>void sort(std::vector<T>& vec)
	{
		std::sort(vec.begin(), vec.end());
	}

	template<class T>auto lower_bound(std::vector<T>const& vec, T v)
	{
		return std::distance(vec.begin(), std::lower_bound(vec.begin(), vec.end(), v));
	}
	template<class T>auto upper_bound(std::vector<T>const& vec, T v)
	{
		return std::distance(vec.begin(), std::upper_bound(vec.begin(), vec.end(), v));
	}

	struct scope_exit
	{
		std::function<void(void)> func;
		scope_exit(std::function<void(void)> f) :func(f)
		{

		}
		~scope_exit()
		{
			func();
		}
	};

	template<int val>using int_tag = std::integral_constant<int, val>;
}

void Main();
int main()	
{
	std::cin.tie(nullptr);
	std::cin.sync_with_stdio(false);
	Main();
}

void Main()
{
	std::int64_t N, T;
	std::cin >> N >> T;
	std::int64_t sum{};
	std::int64_t prev = -T;
	for (std::int64_t i{}; i < N; ++i)
	{
		std::int64_t t;
		std::cin >> t;
		sum += std::min(T, t - prev);
		prev = t;
	}
	std::cout << sum << std::endl;
}