Problem:
Score : 300 points

Problem Statement

There are N boxes arranged in a row.
Initially, the i-th box from the left contains a_i candies.

Snuke can perform the following operation any number of times:

Choose a box containing at least one candy, and eat one of the candies in the chosen box.

His objective is as follows:

Any two neighboring boxes contain at most x candies in total.

Find the minimum number of operations required to achieve the objective.

Constraints

2 ≤ N ≤ 10^5

0 ≤ a_i ≤ 10^9

0 ≤ x ≤ 10^9

Input

The input is given from Standard Input in the following format:

N x
a_1 a_2 ... a_N

Output

Print the minimum number of operations required to achieve the objective.

Sample Input 1

3 3
2 2 2

Sample Output 1

1

Eat one candy in the second box.
Then, the number of candies in each box becomes (2, 1, 2).

Sample Input 2

6 1
1 6 1 2 0 4

Sample Output 2

11

For example, eat six candies in the second box, two in the fourth box, and three in the sixth box.
Then, the number of candies in each box becomes (1, 0, 1, 0, 0, 1).

Sample Input 3

5 9
3 1 4 1 5

Sample Output 3

0

The objective is already achieved without performing operations.

Sample Input 4

2 0
5 5

Sample Output 4

10

All the candies need to be eaten.

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

// 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>

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

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

#define INIT std::ios::sync_with_stdio(false);std::cin.tie(0);
#define VAR(type, ...)type __VA_ARGS__;Scan(__VA_ARGS__);
template<typename T> void Scan(T& t) { std::cin >> t; }
template<typename First, typename...Rest>void Scan(First& first, Rest&...rest) { std::cin >> first; Scan(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);  // 9.22x10^19
constexpr double EPS = 1e-9;
constexpr int MOD = 1000000007;
constexpr double PI = 3.141592653589793238;

signed main() {
	INIT;
	VAR(int, n, x);
	VEC(int, a, n);
	int ans = 0;
	a.emplace_back(0);
	REP(i, n) {
		int t = a[i]+a[i+1] - x;
		if (t <= 0) continue;
		ans += t;
		a[i] -= t;
		a[i + 1] -= t;
	}
	OUT(ans);
	return 0;
}