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 Rust (1.15.1) (judge verdict: Accepted)

use std::cmp::*;
use std::io::*;
use std::str::FromStr;
use utils::*;

pub fn main() {
    let i = stdin();
    let mut o = Vec::new();
    run(i.lock(), &mut o);
    stdout().write_all(&o).unwrap();
}

fn run<R: BufRead, W: Write>(i: R, o: &mut W) {
    let mut i = AtRead::from(i);
    let (n, x) = i.read2::<usize, usize>();
    let a = i.read_vec::<usize>(n);

    writeln!(o, "{}", solve(&a, x)).unwrap();
}
fn solve(a: &[usize], x: usize) -> usize {
    let mut b = Vec::new();
    b.push(0);
    b.push(a[0]);
    for i in 0..a.len() - 1 {
        b.push(a[i] + a[i + 1]);
    }
    b.push(a[a.len() - 1]);
    b.push(0);
    for bi in &mut b {
        if *bi > x {
            *bi = *bi - x;
        } else {
            *bi = 0;
        }
    }

    fn eat(b: &mut usize, value: usize) {
        if *b > value {
            *b -= value;
        } else {
            *b = 0;
        }
    }

    let mut result = 0;
    let mut changed = true;
    while changed {
        changed = false;
        for i in 1..b.len() - 1 {
            let bi = b[i];
            if bi == 0 {
                continue;
            }
            if b[i - 1] == 0 {
                eat(&mut b[i], bi);
                eat(&mut b[i + 1], bi);
                result += bi;
            } else if b[i + 1] == 0 {
                eat(&mut b[i - 1], bi);
                eat(&mut b[i], bi);
                result += bi;
            }
            changed = true;
        }
    }
    result
}

mod utils {
    #![allow(dead_code)]
    use super::*;
    use std::ops::*;

    pub struct AtRead<R: BufRead> {
        r: R,
        s: String,
    }

    macro_rules! fn_read {
        {$f:ident($($v:ident: $t:ident),*)} => {
            pub fn $f<$($t: FromStr),*>(&mut self) -> ($($t),*) {
                let i = &mut self.read_line().split(' ');
                $(
                    let $v = next(i);
                )*
                ($($v),*)
            }
        };
    }

    impl<R: BufRead> AtRead<R> {
        pub fn from(r: R) -> Self {
            AtRead {
                r: r,
                s: String::new(),
            }
        }
        pub fn read_line(&mut self) -> &str {
            self.s.clear();
            self.r.read_line(&mut self.s).unwrap();
            self.s.trim()
        }

        pub fn read<T: FromStr>(&mut self) -> T {
            self.read_line().parse().ok().unwrap()
        }
        fn_read! { read2(v1: T1, v2: T2) }
        fn_read! { read3(v1: T1, v2: T2, v3: T3) }
        fn_read! { read4(v1: T1, v2: T2, v3: T3, v4: T4) }
        fn_read! { read5(v1: T1, v2: T2, v3: T3, v4: T4, v5: T5) }

        pub fn read_vec<T: FromStr>(&mut self, n: usize) -> Vec<T> {
            self.read_line()
                .split(' ')
                .take(n)
                .map(|x| x.parse().ok().unwrap())
                .collect()
        }
        pub fn read_array<A: AsMut<[T]> + Default, T: FromStr>(&mut self) -> A {
            let mut a: A = Default::default();
            {
                let a: &mut [T] = a.as_mut();
                let i = &mut self.read_line().split(' ');
                for n in 0..a.len() {
                    a[n] = next(i);
                }
            }
            a
        }
    }

    fn next<'a, T: FromStr, I: std::iter::Iterator<Item = &'a str>>(i: &mut I) -> T {
        i.next().unwrap().parse().ok().unwrap()
    }

    #[derive(Debug, Clone, Copy)]
    pub struct ModInt(pub usize);

    const MOD_BASE: usize = 1000000007;
    const MOD_INV_POW: usize = 1000000005;

    impl ModInt {
        pub fn new(n: usize) -> Self {
            ModInt(n % MOD_BASE)
        }
        pub fn pow(self, mut exp: usize) -> Self {
            let mut b = self;
            let mut r = ModInt(1);
            while exp != 0 {
                if exp % 2 == 1 {
                    r *= b;
                }
                exp /= 2;
                b = b * b;
            }
            r
        }
        pub fn inverse_element(self) -> Self {
            self.pow(MOD_INV_POW)
        }
    }

    macro_rules! ModInt_op {
        (($ot:ident, $f:ident), ($ot_a:ident, $f_a:ident), $($rhs:ty, $e:expr,)*) => {
            $(
            impl $ot<$rhs> for ModInt {
                type Output = Self;
                fn $f(self, rhs: $rhs) -> Self {
                    Self::new(($e)(self, rhs))
                }
            }
            impl $ot_a<$rhs> for ModInt {
                fn $f_a(&mut self, rhs: $rhs) {
                    *self = Self::new(($e)(*self, rhs))
                }
            }
            )*
        }
    }

    ModInt_op!(
        (Add, add),
        (AddAssign, add_assign),
        ModInt,
        |l: ModInt, r: ModInt| l.0 + r.0,
        usize,
        |l: ModInt, r: usize| l.0 + r,
    );

    ModInt_op!(
        (Mul, mul),
        (MulAssign, mul_assign),
        ModInt,
        |l: ModInt, r: ModInt| l.0 * r.0,
        usize,
        |l: ModInt, r: usize| l.0 * r,
    );

    ModInt_op!(
        (Sub, sub),
        (SubAssign, sub_assign),
        ModInt,
        |l: ModInt, r: ModInt| MOD_BASE + l.0 - r.0,
        usize,
        |l: ModInt, r: usize| MOD_BASE + l.0 - r,
    );

    // std::cmp::Reverseと同じ
    #[derive(PartialEq, Eq)]
    pub struct RevCmp<T>(pub T);

    impl<T: PartialOrd> PartialOrd for RevCmp<T> {
        fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
            other.0.partial_cmp(&self.0)
        }
    }
    impl<T: Ord> Ord for RevCmp<T> {
        fn cmp(&self, other: &Self) -> Ordering {
            other.0.cmp(&self.0)
        }
    }

    pub struct PascalsTriangle<T> {
        buf: Vec<T>,
        n: usize,
    }

    impl<T: One> PascalsTriangle<T> {
        pub fn new(n: usize) -> Self {
            let mut s = PascalsTriangle {
                buf: vec![T::one()],
                n: 1,
            };
            while s.n <= n {
                let i = s.buf.len() - s.n;
                s.buf.push(T::one());
                for m in 1..s.n {
                    let v = s.buf[i + m - 1] + s.buf[i + m];
                    s.buf.push(v);
                }
                s.buf.push(T::one());
                s.n += 1;
            }
            s
        }
        pub fn get(&mut self, n: usize, m: usize) -> T {
            debug_assert!(n <= self.n);
            debug_assert!(m <= n);
            self.buf[n * (n + 1) / 2 + m]
        }
    }

    pub struct PascalsTriangleIter<T> {
        buf: Vec<T>,
    }
    impl<T: One> PascalsTriangleIter<T> {
        pub fn new(n: usize) -> Self {
            let mut s = PascalsTriangleIter {
                buf: Vec::with_capacity(n + 1),
            };
            for _ in 0..n + 1 {
                s.next();
            }
            s
        }
        pub fn next(&mut self) {
            for i in (1..self.buf.len()).rev() {
                self.buf[i] = self.buf[i] + self.buf[i - 1];
            }
            self.buf.push(T::one());
        }
        pub fn get(&self) -> &[T] {
            &self.buf
        }
    }

    pub struct ModIntFacts {
        f: Vec<ModInt>,
        rf: Vec<ModInt>,
    }
    impl ModIntFacts {
        pub fn new(n: usize) -> Self {
            let mut s = ModIntFacts {
                f: vec![ModInt(0); n + 1],
                rf: vec![ModInt(0); n + 1],
            };

            let v = ModInt(1);
            s.f[0] = v;
            for i in 1..n + 1 {
                s.f[i] = s.f[i - 1] * i;
            }
            s.rf[n] = s.f[n].inverse_element();
            for i in (1..n + 1).rev() {
                s.rf[i - 1] = s.rf[i] * i;
            }
            s
        }
        pub fn fact(&self, n: usize) -> ModInt {
            self.f[n]
        }
        pub fn comb(&self, n: usize, c: usize) -> ModInt {
            self.f[n] * self.rf[c] * self.rf[n - c]
        }
    }

    pub trait Zero: Add<Output = Self> + Sized + Copy {
        fn zero() -> Self;
    }
    pub trait One: Zero {
        fn one() -> Self;
    }

    macro_rules! impl_zero {
        ($t:ty, $e:expr) => {
            impl Zero for $t {
                fn zero() -> Self {
                    $e
                }
            }
        }
    }
    macro_rules! impl_one {
        ($t:ty, $e1:expr, $e0:expr) => {
            impl One for $t {
                fn one() -> Self {
                    $e1
                }
            }
            impl_zero!($t, $e0);
        };
    }

    impl_one!(usize, 1, 0);
    impl_one!(u32, 1, 0);
    impl_one!(i32, 1, 0);
    impl_one!(f64, 1.0, 0.0);
    impl_one!(ModInt, ModInt(1), ModInt(0));

    pub trait BinarySearchExt<T> {
        fn lower_bound_by<F: Fn(&T) -> bool>(&self, f: F) -> usize;
        fn lower_bound(&self, x: &T) -> usize;
        fn upper_bound(&self, x: &T) -> usize;
    }
    impl<T: Ord> BinarySearchExt<T> for [T] {
        fn lower_bound_by<F: Fn(&T) -> bool>(&self, f: F) -> usize {
            let mut low = 0;
            let mut high = self.len();
            while low < high {
                let mid = (low + high) / 2;
                if f(&self[mid]) {
                    high = mid;
                } else {
                    low = mid + 1;
                }
            }
            low
        }
        fn lower_bound(&self, x: &T) -> usize {
            self.lower_bound_by(|y| x <= y)
        }
        fn upper_bound(&self, x: &T) -> usize {
            self.lower_bound_by(|y| x < y)
        }
    }

    pub trait AtSliceExt<T> {
        fn rotate(&mut self, mid: usize);
    }
    impl<T> AtSliceExt<T> for [T] {
        fn rotate(&mut self, mid: usize) {
            {
                let (l, r) = self.split_at_mut(mid);
                l.reverse();
                r.reverse();
            }
            self.reverse()
        }
    }

}