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 (Clang 3.8.0) (judge verdict: Accepted)

#include <algorithm>
#include <bitset>
#include <boost/dynamic_bitset.hpp>
#include <cfloat>
#include <cmath>
#include <ctime>
#include <deque>
#include <iomanip>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <typeindex>
#include <typeinfo>
#include <vector>

#define DEBUG(x) cout << #x << ": " << x << endl
#define INFILE() freopen("input.txt", "r", stdin)
#define REP(i, a, b) for (int i = (a); i < (b); i++)
#define REPC(i, a) REP(i, 0, a)
#define ALL(s) begin(s), end(s)
#define RALL(s) rbegin(s), rend(s)

using namespace std;

using ll = long long;
using ull = unsigned long long;
using i_i = pair<int, int>;
using ll_i = pair<ll, int>;
using i_ll = pair<int, ll>;
using d_i = pair<double, int>;
using ll_ll = pair<ll, ll>;
using d_d = pair<double, double>;

static constexpr ll LL_MOD = 1000000009;
static constexpr int I_MOD = 1000000007;
static constexpr double EPS = numeric_limits<double>::epsilon();
static constexpr double PI = 3.14159265358979323846264338327950288;

template <class T> static void scan(vector<T> &v);
static void scan(vector<string> &v, bool isWord = true);
static boost::dynamic_bitset<> scan(char trueValue = 'o');

int main(int argc, char *argv[]) {
  // INFILE();
  ll n, x, count = 0;
  cin >> n >> x;
  vector<ll> c(n);
  scan(c);

  REP(i, 1, n) {
    ll left = c[i - 1] + c[i];

    if (left > x) {
      ll diff = ((left - x) <= c[i]) ? left - x : c[i];
      count += diff;
      c[i] -= diff;
    }
  }

  for (int i = n - 2; i >= 0; i--) {
    ll right = c[i] + c[i + 1];

    if (right > x) {
      ll diff = ((right - x) <= c[i]) ? right - x : c[i];
      count += diff;
      c[i] -= diff;
    }
  }

  cout << count << endl;
  return 0;
}

template <class T> static void scan(vector<T> &v) {
  map<type_index, const char *const> m = {{typeid(int), "%d"},
                                          {typeid(ll), "%lld"},
                                          {typeid(double), "%lf"},
                                          {typeid(char), "%c"}};

  auto tFormat = m[typeid(T)];

  for (T &n : v) {
    scanf(tFormat, &n);
  }
}

static void scan(vector<string> &v, bool isWord) {
  if (isWord) {
    for (auto &n : v) {
      cin >> n;
    }
    return;
  }

  int i = 0, size = v.size();
  string s;
  getline(cin, s);

  if (s.size() != 0) {
    i++;
    v[0] = s;
  }

  for (; i < size; ++i) {
    getline(cin, v[i]);
  }
}

static boost::dynamic_bitset<> scan(char trueValue) {
  string s;
  getline(cin, s);

  if (s.size() == 0) {
    getline(cin, s);
  }

  for_each(begin(s), end(s),
           [trueValue](char &c) { c = (c == trueValue) ? '1' : '0'; });
  return boost::dynamic_bitset<>(string(rbegin(s), rend(s)));
}