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: Wrong Answer)

// - YDK - {{{
#include <functional>
#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <sstream>
#include <numeric>
#include <string>
#include <cstdio>
#include <vector>
#include <tuple>
#include <cmath>
#include <queue>
#include <regex>
#include <set>
#include <map>
using namespace std;
#define eb          emplace_back
#define emp         emplace
#define fi          first
#define se          second
#define debug(...)  fprintf(stderr, __VA_ARGS__ )
#define outl(x)     out < (x) < '\n'
#define outl2(x,y)  out < (x) < ' ' < (y) < '\n'
#define rep(i,n)    for(int i=0; i<(int)(n); ++i)
#define ALL(x)      x.begin(), x.end()
#define ODD(n)      ((n)&1)
#define EVEN(n)     (!ODD(n))
#define _NAMESPACE_YDK_ namespace ydk {
#define _END_NAMESPACE_ }
template<class A, class B>inline bool chmax(A &a, B b){return b>a ? a=b,1 : 0;}
template<class A, class B>inline bool chmin(A &a, B b){return b<a ? a=b,1 : 0;}
template<class T>using MinHeap = priority_queue< T, vector<T>, greater<T> >;
using ll  = long long;
using pii = pair<int, int>;
inline bool inside(int x, int y, int W, int H) { return x>=0 && y>=0 && x<W && y<H; }
constexpr int       INF  = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr int dx[] = {1, 0, -1, 0};
constexpr int dy[] = {0, 1, 0, -1};
struct Point: public pii {
    int &x = this->first,   &y = this->second;
    explicit Point(int x=0, int y=0): pii(x, y) {}
};
struct Writer
{
    static constexpr size_t BUFF_SIZE = 1 << 18;
    static char _buf[BUFF_SIZE];
    explicit Writer() { setvbuf(stdout, _buf, _IOFBF, sizeof(_buf)); }
    inline void    ln()         {putchar('\n');}
    inline Writer& operator() (int n)   {printf("%d", n);                return *this;}
    inline Writer& operator() (ll  n)   {printf("%lld", n);              return *this;}
    inline Writer& operator() (char c)  {printf("%c", c);                return *this;}
    inline Writer& operator() (double d){printf("%lf", d);               return *this;}
    inline Writer& operator() (const char* s){printf("%s", s);           return *this;}
    inline Writer& operator() (const string &s){printf("%s", s.c_str()); return *this;}
    inline Writer& operator() (bool f)  {printf("%s", f?"true":"false"); return *this;}
    inline Writer& operator() (void)  {putchar('\n'); return *this;}

    template<class InputIterator>
    inline Writer& operator() (InputIterator first, InputIterator last, const char *space=" ")
    {
        for(; first != last; ++first) {
            (*this)(*first);
            printf("%s", (first+1 == last)? "\n" : space);
        }
        return *this;
    }
};
char Writer::_buf[BUFF_SIZE];
template<class T> inline Writer& operator < (Writer &o, const T &v) { return o(v); }

struct Scanner
{
    char tmp[65536];
    inline Scanner& read(int &n)    {scanf("%d", &n);       return *this;}
    inline Scanner& read(ll  &n)    {scanf("%lld", &n);     return *this;}
    inline Scanner& read(char &c)   {scanf(" %c", &c);      return *this;}
    inline Scanner& read(double &d) {scanf("%lf", &d);      return *this;}
    inline Scanner& read(char *s)   {scanf("%s", s);        return *this;}
    inline Scanner& read(string &s) {scanf("%s",tmp); s=string(tmp); return*this;}
};
template<class T> inline Scanner& operator > (Scanner &in, T &v) { return in.read(v); }
template<class T> inline Scanner& operator , (Scanner &in, T &v) { return in.read(v); }
Writer  out;
Scanner in;
// }}}

_NAMESPACE_YDK_

constexpr int LIM = (int)1e5 * 2;

int N, x;
ll a[LIM];
ll b[LIM];

signed main(void)
{
    in> N, x;
    rep(i, N) {
        in> a[i];
    }

    ll ans = 0;

    rep(i, N-1) {
        ll s = a[i]+a[i+1];
        if (s <= x) continue;
        ans += s - x;
        a[i+1] -= (s-x);
    }

    outl(ans);

    return 0;
}

_END_NAMESPACE_

signed main(void) { return ydk::main(); }

//--------END--------