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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;
 
class Main{

    void solve(){
        int N = ni();
        int x = ni();
        long[] a = new long[N];
        for(int i = 0; i < N; i++){ 
            a[i] = nl();
        }

        if(N == 2){
            System.out.println(max(0, a[0] + a[1] - x));
        } else {
            long ans = 0;
            for(int i = 0; i < N - 2; i++){
                long left = a[i];
                long mid = a[i + 1];
                long right = a[i + 2];
                if(left + mid <= x && mid + right <= x){
                    continue;
                } else if(left + mid <= x){
                    long eat = mid + right - x;
                    if(a[i + 2] >= eat){
                        a[i + 2] -= eat;
                        ans += eat;
                    } else {
                        ans += a[i + 2];
                        eat -= a[i + 2];
                        a[i + 2] = 0;
                        ans += eat;
                        a[i + 1] -= eat;

                    }
                } else if(mid + right <= x){
                    long eat = left + mid - x;
                    if(a[i] >= eat){
                        a[i] -= eat;
                        ans += eat;
                    } else {
                        ans += a[i];
                        eat -= a[i];
                        a[i] = 0;
                        ans += eat;
                        a[i - 1] -= eat;
                    }

                } else {
                    long eat = max(left + mid - x, mid + right - x);
                    long lefteat = left + mid - x;
                    long righteat = mid + right - x;
                    if(a[i + 1] >= eat){
                        a[i + 1] -= eat;
                        ans += eat;
                    } else {
                        ans += a[i + 1];
                        lefteat -= a[i + 1];
                        righteat -= a[i + 1];
                        a[i + 1] = 0;

                        if(righteat > 0 && a[i + 2] >= righteat){
                            a[i + 2] -= righteat;
                            ans += righteat;
                        } else if(righteat > 0) {
                            ans += a[i + 2];
                            righteat -= a[i + 2];
                            a[i + 2] = 0;
                        }
                        if(lefteat > 0 && a[i] >= lefteat){
                            a[i] -= lefteat;
                            ans += lefteat;
                        } else if(lefteat > 0) {
                            ans += a[i];
                            lefteat -= a[i];
                            a[i] = 0;
                        }
                    }

                }
            }
            System.out.println(ans);
        }


    } 

    public static void main(String[] args){
        new Main().solve();
    }

    private FastScanner scan = new FastScanner();
    private final int MOD = 1_000_000_007;
    private final int INF = 2147483647;
    private final long LINF = 9223372036854775807L;
    private long[] fac;
    private long[] finv;
    private long[] inv;

    // Scanner
    int ni(){ return scan.nextInt();}
    int[] ni(int n){int[] a = new int[n]; for(int i = 0; i < n; i++){a[i] = ni();} return a;}
    int[][] ni(int y, int x){int[][] a = new int[y][x];
        for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = ni();}} return a;}
    long nl(){return scan.nextLong();}
    long[] nl(int n){long[] a = new long[n]; for(int i = 0; i < n; i++){a[i] = nl();} return a;}
    long[][] nl(int y, int x){long[][] a = new long[y][x];
        for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = nl();}} return a;}
    String ns(){return scan.next();}
    String[] ns(int n){String[] a = new String[n]; for(int i = 0; i < n; i++){a[i] = ns();} return a;}
    String[][] ns(int y, int x){String[][] a = new String[y][x];
        for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = ns();}} return a;}

    // Mathematics
    int max(int a, int b){return Math.max(a, b);}
    long max(long a, long b){return Math.max(a, b);}
    double max(double a, double b){return Math.max(a, b);}
    int max(int[] a){int max = a[0]; for(int value:a){max = max(max,value);} return max;}
    long max(long[] a){long max = a[0]; for(long value:a){max = max(max,value);} return max;}
    double max(double[] a){double max = a[0]; for(double value:a){max = max(max,value);} return max;}
    int min(int a, int b){return Math.min(a, b);}
    long min(long a, long b){return Math.min(a, b);}
    double min(double a, double b){return Math.min(a, b);}
    int min(int[] a){int min = a[0]; for(int value:a){min = min(min,value);} return min;}
    long min(long[] a){long min = a[0]; for(long value:a){min = min(min,value);} return min;}
    double min(double[] a){double min = a[0]; for(double value:a){min = min(min,value);} return min;}
    long sum(int[] a){long sum = 0; for(int value:a){sum += value;} return sum;}
    long sum(long[] a){long sum = 0; for(long value:a){sum += value;} return sum;}
    double sum(double[] a){double sum = 0; for(double value:a){sum += value;} return sum;}
    int gcd(int a, int b){return b == 0 ? a : gcd(b, a % b);}
    long gcd(long a, long b){return b == 0 ? a : gcd(b, a % b);}
    int lcm(int a, int b){return a / gcd(a, b) * b;}
    long lcm(long a, long b){return a / gcd(a, b) * b;}
    long fact(int n){ if(n == 0){ return 1; } long a = n; for(long i = n - 1; i >= 2; i--){ a = a % MOD * i; } return a; }
    long fact(long n){ if(n == 0){ return 1; } long a = n; for(long i = n - 1; i >= 2; i--){ a = a % MOD * i; } return a; }
    // nPr(int)
    long npr(int n, int r){
        long a = 1;
        for(int i = n; i > n - r; i--){
            a *= i;
        }
        return a;
    }
    // nPr(long)
    long npr(long n, long r){
        long a = 1;
        for(long i = n; i > n - r; i--){
            a *= i;
        }
        return a;
    }
    // 素数判定(int)
    boolean checkPrime(int n){
        for(int i = 2; i * i <= n; i++){
            if(n % i == 0){
                return false;
            }
        }
        return true;
    }
    // 素数判定(long)
    boolean checkPrime(long n){
        for(long i = 2; i * i <= n; i++){
            if(n % i == 0){
                return false;
            }
        }
        return true;
    }
    // エラトステネスの篩
    List<Integer> erathos(int n){
        boolean[] flag = new boolean[n + 1];
        List<Integer> nums = new ArrayList<>();
        for(int i = 2; i <= n; i++){
            if(flag[i]) continue;
            nums.add(i);
            for(int j = i * 2; j <= n; j += i){
                flag[j] = true;
            }
        }

        return nums;
    }

    // mod pにおける累乗 a^n
    long modpow(long a, long n, long p){
        long res = 1;
        while(n > 0){
            if((n & 1) == 1){
                res = res * a % p;
            }
            a = a * a % p;
            n = n >> 1;
        }
        return res;
    }
    // mod pにおけるaの逆元a^-1
    long modinv(long a, long p){
        return modpow(a, p - 2, p);
    }
    // fac,finv,invの初期化
    void comInit(int max){
        fac = new long[max];
        finv = new long[max];
        inv = new long[max];
        fac[0] = fac[1] = 1;
        finv[0] = finv[1] = 1;
        inv[1] = 1;
        for(int i = 2; i < max; i++){
            fac[i] = fac[i - 1] * i % MOD;
            inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
            finv[i] = finv[i - 1] * inv[i] % MOD;
        }
    }
    // 二項係数nCr
    long com(int n, int r){
        if(n < r || (n < 0 || r < 0)){
            return 0;
        }
        return fac[n] * (finv[r] * finv[n - r] % MOD) % MOD;
    }
    // 二項係数nCr（nが10^9など巨大なとき用）
    long ncr(long n, long k){
        long a = 1;
        long b = 1;
        for(int i = 1; i <= k; i++){
            a = a * (n + 1 - i) % MOD;
            b = b * i % MOD;
        }
        
        return modinv(b, MOD) * a % MOD;
    }
    // 二次元上の二点間の距離
    double distance(double x1, double y1, double x2, double y2){
        double dist = Math.sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
        return dist;
    }
    // 三次元上の二点間の距離
    double distance(double x1, double y1, double z1, double x2, double y2, double z2){
        double dist = Math.sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2) + (z1 - z2) * (z1 - z2));
        return dist;
    }


    // Array
    void sort(int[] a){ Arrays.sort(a);}
    void sort(long[] a){ Arrays.sort(a);}
    void sort(double[] a){ Arrays.sort(a);}
    void sort(String[] a){ Arrays.sort(a);}
    int[] reverse(int[] a){
        int[] reversed = new int[a.length];
        for(int i = 0; i < a.length; i++){
            reversed[a.length - i - 1] = a[i];
        }
        return reversed;
    }
    long[] reverse(long[] a){
        long[] reversed = new long[a.length];
        for(int i = 0; i < a.length; i++){
            reversed[a.length - i - 1] = a[i];
        }
        return reversed;
    }
    double[] reverse(double[] a){
        double[] reversed = new double[a.length];
        for(int i = 0; i < a.length; i++){
            reversed[a.length - i - 1] = a[i];
        }
        return reversed;
    }
    char[] reverse(char[] a){
        char[] reversed = new char[a.length];
        for(int i = 0; i < a.length; i++){
            reversed[a.length - i - 1] = a[i];
        }
        return reversed;
    }
    String[] reverse(String[] a){
        String[] reversed = new String[a.length];
        for(int i = 0; i < a.length; i++){
            reversed[a.length - i - 1] = a[i];
        }
        return reversed;
    }
    boolean[] reverse(boolean[] a){
        boolean[] reversed = new boolean[a.length];
        for(int i = 0; i < a.length; i++){
            reversed[a.length - i - 1] = a[i];
        }
        return reversed;
    }
    void fill(int[] array, int x) { Arrays.fill(array, x); }
    void fill(long[] array, long x) { Arrays.fill(array, x); }
    void fill(double[] array, double x) { Arrays.fill(array, x); }
    void fill(boolean[] array, boolean x) { Arrays.fill(array, x); }
    void fill(int[][] array, int x) { for(int a[] : array) { fill(a, x); } }
    void fill(long[][] array, long x) { for(long a[] : array) { fill(a, x); } }
    void fill(double[][] array, double x) { for(double a[] : array) { fill(a, x); } }
    void fill(boolean[][] array, boolean x) { for(boolean a[] : array) { fill(a, x); } }
    void fill(int[][][] array, int x) { for(int[][] ary : array) { for(int[] a : ary){ fill(a, x); } } }
    void fill(long[][][] array, long x) { for(long[][] ary : array) { for(long[] a : ary){ fill(a, x); } } }

    // Algorithm
    // 深さ優先探索
    void dfs(Node[] nodes, int v, boolean[] seen){
        seen[v] = true;
        
        for(Edge edge : nodes[v].edges){
            if(seen[edge.to]) continue;
            dfs(nodes, edge.to, seen);
        }

    }
    // 幅優先探索
    long[] bfs(Node[] nodes, int start){
        Queue<Integer> queue = new ArrayDeque<>();
        queue.add(start);
        long[] dist = new long[nodes.length];
        fill(dist, -1);
        dist[start] = 0;

        while(!queue.isEmpty()){
            int now = queue.poll();
            for(Edge edge : nodes[now].edges){
                if(dist[edge.to] != -1) continue;
                dist[edge.to] = dist[now] + 1;
                queue.add(edge.to);
            }
        }

        return dist;
    }
    
    // ダイクストラ法
    long[] dijkstra(Node[] nodes, int start){
        Queue<Edge> queue = new PriorityQueue<>();
        long[] dist = new long[nodes.length];
        fill(dist, LINF / 2);
        dist[start] = 0;
        queue.add(new Edge(start, start, dist[start]));

        while(!queue.isEmpty()){
            Edge now = queue.poll();        
            if(dist[now.to] < now.cost) continue;
            for(Edge edge : nodes[now.to].edges){
                if(dist[edge.to] > dist[edge.from] + edge.cost){
                    dist[edge.to] = dist[edge.from] + edge.cost;
                    queue.add(new Edge(edge.from, edge.to, dist[edge.to]));
                    nodes[edge.to].past = edge.from;
                }
            }
        }

        return dist;
    }
    
    // ソート済みint型配列でkey以上の値の最小indexを返す
    int lowerBound(int[] a, int key){
        int ng = -1;
        int ok = a.length;
        while(Math.abs(ok - ng) > 1){
            int mid = (ok + ng) / 2; 
            if(a[mid] >= key){
                ok = mid;
            } else {
                ng = mid;
            }
        }
        return ok;
    }
    // ソート済みlong型配列でkey以上の値の最小indexを返す
    int lowerBound(long[] a, long key){
        int ng = -1;
        int ok = a.length;
        while(Math.abs(ok - ng) > 1){
            int mid = (ok + ng) / 2; 
            if(a[mid] >= key){
                ok = mid;
            } else {
                ng = mid;
            }
        }
        return ok;
    }
    // 文字列sとtの最長共通部分列の長さを返す
    int lcs(String s , String t){
        int[][] dp = new int[s.length() + 1][t.length() + 1];

        for(int i = 0; i < s.length(); i++){
            for(int j = 0; j < t.length(); j++){
                if(s.charAt(i) == t.charAt(j)){
                    dp[i + 1][j + 1] = max(dp[i][j] + 1, dp[i + 1][j + 1]);
                }
                dp[i + 1][j + 1] = max(dp[i + 1][j + 1], dp[i + 1][j]);
                dp[i + 1][j + 1] = max(dp[i + 1][j + 1], dp[i][j + 1]);
            }
        }

        return dp[s.length()][t.length()];
    }

}

// ノード
class Node{
    int id;             // ノード番号
    int past;           // 直前の頂点
    List<Edge> edges;   // 辺のリスト

    Node(int id, int past){
        this.id = id;
        this.past = past;
        this.edges = new ArrayList<>();
    }
    void addEdge(Edge edge){
        edges.add(edge);
    }

    public boolean equals(Object obj){
        if(obj instanceof Node){
            Node node = (Node)obj;
            return this.id == node.id;
        } 
        return false;
    }
    public int hashCode(){
        return id;
    }
    public String toString(){
        return "[id:" + id + " past: " + past + "]";
    }
}

// 辺の情報を持つクラス
class Edge implements Comparable<Edge>{
    int from;       // どの頂点から
    int to;          //  どの頂点へ
    long cost;       // 辺の重み

    Edge(int from, int to, long cost){
        this.from = from;
        this.to = to;
        this.cost = cost;
    }
    public int compareTo(Edge edge){
        return Long.compare(this.cost, edge.cost);
    }

    public String toString(){
        return "[" + from + " to " + to + " cost:" + cost + "]";
    }
}
// 辺の重み比較のComparator
class EdgeComparator implements Comparator<Edge>{
    @Override
    public int compare(Edge e1, Edge e2){
        long cost1 = e1.cost;
        long cost2 = e2.cost;
        if(cost1 < cost2){
            return -1;
        } else if(cost1 > cost2){
            return 1;
        } else {
            return 0;
        }
    }
}
// Union-Find
class UnionFind{
    int[] par;
    int[] size;
    UnionFind(int N){
        par = new int[N];
        size = new int[N];
        for(int i = 0; i < N; i++){
            par[i] = i;
            size[i] = 1;
        }
    }

    void init(int N){
        for(int i = 0; i < N; i++){
            par[i] = i;
            size[i] = 1;
        }
    }

    int root(int x){
        if(par[x] == x){
            return x;
        } else {
            return par[x] = root(par[x]);
        }
    }

    boolean same(int x, int y){
        return root(x) == root(y);
    }

    void unite(int x, int y){
        x = root(x);
        y = root(y);
        if(x == y) return;
        if(size[x] < size[y]){
            int tmp = x;
            x = y;
            y = tmp;
        }
        size[x] += size[y];
        par[y] = x;
    }

    int size(int x){
        return size[root(x)];
    }

}

// 順列を管理する
class Permutation {
    private int number;
    private int listSize;
    private int searched;
    private int nextIndex;
    private int[][] permList;

    Permutation(int num) {
        this.number = num;
        this.listSize  = this.fact(this.number);
        this.searched   = 0;
        this.nextIndex = 0;
        this.permList  = new int[this.listSize][this.number];

        this.create(0, new int[this.number], new boolean[this.number]);
    }

    int[] nextPerm() {
        return permList[this.nextIndex++];
    }

    boolean isNext() {
        if(this.nextIndex < this.listSize) {
            return true;
        } else {
            this.nextIndex = 0;
            return false;
        }
    }

    int fact(int n){
        return n == 0 ? 1 : n * fact(n-1);
    }

    void create(int num, int[] list, boolean[] flag) {
        if(num == this.number) {
            copyArray(list, permList[this.searched]);
            this.searched++;
        }
        for(int i = 0; i < this.number; i++){
            if(flag[i]) continue;
            list[num] = i;
            flag[i] = true;
            this.create(num+1, list, flag);
            flag[i] = false;

        }
    }

    void copyArray(int[] from, int[] to) {
        for(int i=0; i<from.length; i++) to[i] = from[i];
    }

    void printNum(int[] nums) {
        for(int n : nums) System.out.print(n);
        System.out.println();
    }
}

// 一点更新区間取得Segment Tree
class SegTree{
    int[] dat;
    int size;
    
    SegTree(int N){
        this.dat = new int[N * 4];
        this.size = N;
    }

    // [a, b]の最小値を返す
    // l,rにはノードkに対応する区間を与える
    int query(int a, int b, int k, int l, int r){
        if(r < a || b < l) return Integer.MAX_VALUE;
        if(a <= l && r <= b) return dat[k];
        int vl = query(a, b, k << 1, l, (l + r) / 2);
        int vr = query(a, b, (k << 1) + 1, (l + r) / 2 + 1, r);
        return Math.min(vl, vr);
    }

    // インデックスiの値をxに更新
    void update(int i, int x){
        i += this.size - 1;
        dat[i] = x;
        while(i > 0){
            i = i >> 1;     // 1ビットぶん右シフト
            dat[i] = Math.min(dat[i << 1], dat[(i << 1) + 1]);
        }
    }

    public String toString(){
        StringBuilder sb = new StringBuilder("[");
        for(int i = size; i < 2 * size; i++){
            sb.append(dat[i]).append(",");
        }
        sb.delete(sb.length() - 1, sb.length());
        String output = sb.append("]").toString();
        return output;
    }
}

// Range Sum Queryを実現するBinary Indexed Tree
class BIT{
    int[] tree;

    BIT(int N){
        this.tree = new int[N + 1];
    }

    int sum(int i){
        int sum = 0;
        while(i > 0){
            sum += this.tree[i];
            i -= i & -i;
        }
        return sum;
    }

    void add(int i, int x){
        while(i <= tree.length){
            this.tree[i] += x;
            i += i & -i;
        }
    }

    public String toString(){
        StringBuilder sb = new StringBuilder("[");
        for(int i = 0; i < tree.length; i++){
            sb.append(tree[i] + ",");
        }
        sb.append("]");
        String output = sb.toString();
        return output;
    }
    
}

// 標準のScannerより高速に標準入力する
class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() { return Double.parseDouble(next());}
}