Enough is enough. Too many times it happened that Vasya forgot to dispose of garbage and his apartment stank afterwards. Now he wants to create a garbage disposal plan and stick to it.

For each of next n days Vasya knows a_i — number of units of garbage he will produce on the i-th day. Each unit of garbage must be disposed of either on the day it was produced or on the next day. Vasya disposes of garbage by putting it inside a bag and dropping the bag into a garbage container. Each bag can contain up to k units of garbage. It is allowed to compose and drop multiple bags into a garbage container in a single day.

Being economical, Vasya wants to use as few bags as possible. You are to compute the minimum number of bags Vasya needs to dispose of all of his garbage for the given n days. No garbage should be left after the n-th day.

Input

The first line of the input contains two integers n and k (1 ≤ n ≤ 2⋅10^5, 1 ≤ k ≤ 10^9) — number of days to consider and bag's capacity. The second line contains n space separated integers a_i (0 ≤ a_i ≤ 10^9) — the number of units of garbage produced on the i-th day.

Output

Output a single integer — the minimum number of bags Vasya needs to dispose of all garbage. Each unit of garbage should be disposed on the day it was produced or on the next day. No garbage can be left after the n-th day. In a day it is allowed to compose and drop multiple bags.

Examples

Input

3 2
3 2 1


Output

3


Input

5 1
1000000000 1000000000 1000000000 1000000000 1000000000


Output

5000000000


Input

3 2
1 0 1


Output

2


Input

4 4
2 8 4 1


Output

4
import java.util.*;
import java.awt.List;
import java.io.*;
import java.lang.*;
import java.lang.reflect.Array;
public class code10 {

    public static int[] stree = new int[1000000];
    public static int[] sctree = new int[1000000];
    public static int[] smtree = new int[1000000];
    
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);

        // Code starts..

        
        
        int n = in.nextInt();
        long k = in.nextLong();
        long[] a = new long[n];
        for(int i=0; i<n; i++)
        	a[i] = in.nextLong();
        long ans = 0;
        for(int i=n-1; i>=0; i--)
        {
        	
        	long cur = (long)Math.ceil(a[i]/(double)k);
        	long tot = cur*k;
        	ans += cur;
        	if(i-1>=0)
        	{
        		
        		a[i-1] = Math.max(0, a[i-1] - (tot - a[i]));
        	}
        	
        	
        }
        pw.println(ans);
        
  
        // code ends...

        pw.flush();
        pw.close();
    }

    
    
    

    public static long[][] mul(long[][] a, long[][] b){
        
        
        int n = a.length;
        int m = b[0].length;
        long[][] c = new long[n][m];
        
        for(int i=0; i<n; i++)
            for(int j=0; j<m; j++)
            {
                long tmp = 0;
                for(int k=0; k<a[0].length; k++)
                    tmp =( (tmp+mod)%mod+(a[i][k]*b[k][j]+mod)%mod)%mod;
                c[i][j] = (tmp+mod)%mod;
            }
        
        return c;
    }
    
    
    
    public static long[][] pow(long[][] a,int  n)
    {
        
        long[][] res = a;
        while(n>0)
        {
            if(n%2==1)
            {
                res = mul(a, res);
            }
            
            a = mul(a, a);
            
            n/=2;
            
            
        }
        
        return res;
        
        
    }
    
    
    
    
    

    
    
    

    
    public static boolean isSubSequence(char[] str2, String str1) {

        int j = 0;
        int m = str1.length();
        int n = str2.length;

        for (int i = 0; i < n && j < m; i++)

            if (str1.charAt(j) == str2[i])

                j++;

        return (j == m);
    }

    static class InputReader {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int snext() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        public String readString() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public String nextLine() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    public static long c = 0;

    public static long mod = (long)Math.pow(10, 6)+3;
    public static int d;
    public static int p;
    public static int q;
    public static boolean flag;
    //public static long INF = Long.MAX_VALUE;

    public static void factSieve(int[] fact, long n) {

        for (int i = 2; i <= n; i += 2)
            fact[i] = 2;

        for (int i = 3; i <= n; i += 2) {
            if (fact[i] == 0) {
                fact[i] = i;

                for (int j = i; (long) j * i <= n; j++) {
                    fact[(int) ((long) i * j)] = i;
                }
            }
        }

        /*
         * int k = 1000; while(k!=1) { System.out.print(a[k]+" "); k /= a[k];
         * 
         * }
         */
    }

    public static long floorsqrt(long n) {
        long ans = 0;
        long l = 0;
        long r = n;
        long mid = 0;
        while (l <= r) {
            mid = (l + r) / 2;
            if (mid * mid == n)
                return mid;

            if (mid * mid > n) {
                r = mid - 1;
            } else {
                ans = mid;
                l = mid + 1;
            }

        }

        return ans;
    }

    public static long fun(int[] a, int[] b, int m, int n) {
        long result = 0;
        for (int i = 0; i < m; i++)
            for (int j = 0; j < m; j++) {
                long[] fib = new long[Math.max(2, n + 2)];
                fib[1] = a[i];
                fib[2] = b[j];
                for (int k = 3; k <= n; k++)
                    fib[k] = (fib[k - 1] % mod + fib[k - 2] % mod) % mod;
                result = (result % mod + fib[n] % mod) % mod;
            }

        return result;

    }

    /*
     * public static double slope(pair p1, pair p2) { double m = INF; if((p1.x -
     * p2.x)!=0) m = p1.y - p2.y/(p1.x - p2.x);
     * 
     * 
     * return Math.abs(m);
     * 
     * }
     */

    public static int count(String[] s, int f) {
        int count = 0;
        int n = s[0].length();

        if (f == 1) {
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (i % 2 == 0) {
                        if (j % 2 == 0 && s[i].charAt(j) == '0')
                            count++;
                        if (j % 2 == 1 && s[i].charAt(j) == '1')
                            count++;
                    }
                    if (i % 2 == 1) {
                        if (j % 2 == 1 && s[i].charAt(j) == '0')
                            count++;
                        if (j % 2 == 0 && s[i].charAt(j) == '1')
                            count++;
                    }

                }
            }
        } else {

            count = 0;

            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (i % 2 == 1) {
                        if (j % 2 == 0 && s[i].charAt(j) == '0')
                            count++;
                        if (j % 2 == 1 && s[i].charAt(j) == '1')
                            count++;
                    }
                    if (i % 2 == 0) {
                        if (j % 2 == 1 && s[i].charAt(j) == '0')
                            count++;
                        if (j % 2 == 0 && s[i].charAt(j) == '1')
                            count++;
                    }

                }
            }

        }

        return count;

    }

    public static int gcd(int p2, int p22) {
        if (p2 == 0)
            return (int) p22;
        return gcd(p22 % p2, p2);
    }

    public static int findGCD(int arr[], int n) {
        int result = arr[0];
        for (int i = 1; i < n; i++)
            result = gcd(arr[i], result);

        return result;
    }

    public static void nextGreater(long[] a, int[] ans) {

        Stack<Integer> stk = new Stack<>();
        stk.push(0);

        for (int i = 1; i < a.length; i++) {

            if (!stk.isEmpty()) {
                int s = stk.pop();
                while (a[s] < a[i]) {
                    ans[s] = i;
                    if (!stk.isEmpty())
                        s = stk.pop();
                    else
                        break;
                }
                if (a[s] >= a[i])
                    stk.push(s);
            }

            stk.push(i);

        }
        return;

    }

    public static void nextGreaterRev(long[] a, int[] ans) {

        int n = a.length;
        int[] pans = new int[n];
        Arrays.fill(pans, -1);
        long[] arev = new long[n];
        for (int i = 0; i < n; i++)
            arev[i] = a[n - 1 - i];

        Stack<Integer> stk = new Stack<>();
        stk.push(0);

        for (int i = 1; i < n; i++) {

            if (!stk.isEmpty()) {
                int s = stk.pop();
                while (arev[s] < arev[i]) {
                    pans[s] = n - i - 1;
                    if (!stk.isEmpty())
                        s = stk.pop();
                    else
                        break;
                }
                if (arev[s] >= arev[i])
                    stk.push(s);
            }

            stk.push(i);

        }

        // for(int i=0; i<n; i++)
        // System.out.print(pans[i]+" ");

        for (int i = 0; i < n; i++)
            ans[i] = pans[n - i - 1];

        return;

    }

    public static void nextSmaller(long[] a, int[] ans) {

        Stack<Integer> stk = new Stack<>();
        stk.push(0);

        for (int i = 1; i < a.length; i++) {

            if (!stk.isEmpty()) {
                int s = stk.pop();
                while (a[s] > a[i]) {
                    ans[s] = i;
                    if (!stk.isEmpty())
                        s = stk.pop();
                    else
                        break;
                }
                if (a[s] <= a[i])
                    stk.push(s);
            }

            stk.push(i);

        }
        return;

    }

    public static long lcm(int[] numbers) {
        long lcm = 1;
        int divisor = 2;
        while (true) {
            int cnt = 0;
            boolean divisible = false;
            for (int i = 0; i < numbers.length; i++) {
                if (numbers[i] == 0) {
                    return 0;
                } else if (numbers[i] < 0) {
                    numbers[i] = numbers[i] * (-1);
                }
                if (numbers[i] == 1) {
                    cnt++;
                }
                if (numbers[i] % divisor == 0) {
                    divisible = true;
                    numbers[i] = numbers[i] / divisor;
                }
            }
            if (divisible) {
                lcm = lcm * divisor;
            } else {
                divisor++;
            }
            if (cnt == numbers.length) {
                return lcm;
            }
        }
    }

    public static long fact(long n) {

        long factorial = 1;
        for (int i = 1; i <= n; i++) {
            factorial *= i;
        }
        return factorial;
    }

    public static int lowerLimit(int[] a, int n) {
        int ans = 0;

        int ll = 0;
        int rl = a.length - 1;
        // System.out.println(a[rl]+" "+n);
        if (a[0] > n)
            return 0;
        if (a[0] == n)
            return 1;
        else if (a[rl] <= n)
            return rl + 1;

        while (ll <= rl) {

            int mid = (ll + rl) / 2;
            if (a[mid] == n) {
                ans = mid + 1;
                break;
            }

            else if (a[mid] > n) {
                rl = mid - 1;

            } else {
                ans = mid + 1;
                ll = mid + 1;
            }
        }

        return ans;
    }

    public static long choose(long total, long choose) {
        if (total < choose)
            return 0;
        if (choose == 0 || choose == total)
            return 1;
        return (choose(total - 1, choose - 1) + choose(total - 1, choose)) % mod;
    }

    public static int[] suffle(int[] a, Random gen) {
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int ind = gen.nextInt(n - i) + i;
            int temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }
        return a;
    }

    public static pair[] suffle(pair[] a, Random gen) {
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int ind = gen.nextInt(n - i) + i;
            pair temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }
        return a;
    }
    
    
    
    
    public static int floorSearch(int arr[], int low, int high, int x) {
        if (low > high)
            return -1;

        if (x > arr[high])
            return high;
        int mid = (low + high) / 2;

        if (mid > 0 && arr[mid - 1] < x && x < arr[mid])
            return mid - 1;

        if (x < arr[mid])
            return floorSearch(arr, low, mid - 1, x);

        return floorSearch(arr, mid + 1, high, x);
    }

    public static void swap(int a, int b) {
        int temp = a;
        a = b;
        b = temp;
    }

    public static ArrayList<Integer> primeFactorization(int n) {
        ArrayList<Integer> a = new ArrayList<Integer>();
        for (int i = 2; i * i <= n; i++) {
            while (n % i == 0) {
                a.add(i);
                n /= i;
            }
        }
        if (n != 1)
            a.add(n);
        return a;
    }
    
    
    

    public static void sieve(boolean[] isPrime, int n) {
        for (int i = 1; i < n; i++)
            isPrime[i] = true;

        isPrime[0] = false;
        isPrime[1] = false;

        for (int i = 2; i * i < n; i++) {
            if (isPrime[i] == true) {
                for (int j = (2 * i); j < n; j += i)
                    isPrime[j] = false;
            }
        }
    }

    public static int lowerbound(ArrayList<Long> net, long c2) {
        int i = Collections.binarySearch(net, c2);
        if (i < 0)
            i = -(i + 2);
        return i;

    }
    
    public static int lowerboundArray(int[] dis, int c2) {
        int i = Arrays.binarySearch(dis, c2);
        if (i < 0)
            i = -(i + 2);
        return i;

    }

    public static int uperbound(ArrayList<Integer> list, int c2) {
        int i = Collections.binarySearch(list, c2);
        if (i < 0)
            i = -(i + 1);
        return i;

    }

    public static int uperboundArray(int[] dis, int c2) {
        int i = Arrays.binarySearch(dis, c2);
        if (i < 0)
            i = -(i + 1);
        return i;

    }

    public static long[] sort(long[] a) {
        Random gen = new Random();
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int ind = gen.nextInt(n - i) + i;
            long temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }

        Arrays.sort(a);
        return a;
    }

    public static int[] sort(int[] a) {
        Random gen = new Random();
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int ind = gen.nextInt(n - i) + i;
            int temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }

        Arrays.sort(a);
        return a;
    }

    public static int GCD(int a, int b) {
        if (b == 0)
            return a;
        else
            return GCD(b, a % b);
    }

    public static long GCD(long a, long b) {
        if (b == 0)
            return a;
        else
            return GCD(b, a % b);
    }

    public static void extendedEuclid(int A, int B) {
        if (B == 0) {
            d = A;
            p = 1;
            q = 0;
        } else {
            extendedEuclid(B, A % B);
            int temp = p;
            p = q;
            q = temp - (A / B) * q;
        }
    }

    public static long LCM(long a, long b) {
        return (a * b) / GCD(a, b);
    }

    public static int LCM(int a, int b) {
        return (a * b) / GCD(a, b);
    }

    public static int binaryExponentiation(int x, int n) {
        int result = 1;
        while (n > 0) {
            if (n % 2 == 1)
                result = result * x;
            x = x * x;
            n = n / 2;
        }
        return result;
    }

    public static int[] countDer(int n) {
        int der[] = new int[n + 1];

        der[0] = 1;
        der[1] = 0;
        der[2] = 1;

        for (int i = 3; i <= n; ++i)
            der[i] = (i - 1) * (der[i - 1] + der[i - 2]);

        // Return result for n
        return der;
    }

    static long binomialCoeff(int n, int k) {
        long C[][] = new long[n + 1][k + 1];
        int i, j;

        // Calculate value of Binomial Coefficient in bottom up manner
        for (i = 0; i <= n; i++) {
            for (j = 0; j <= Math.min(i, k); j++) {
                // Base Cases
                if (j == 0 || j == i)
                    C[i][j] = 1;

                // Calculate value using previosly stored values
                else
                    C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
            }
        }

        return C[n][k];
    }

    public static long binaryExponentiation(long x, long n) {
        long result = 1;
        while (n > 0) {
            if (n % 2 == 1)
                result = result * x;
            x = (x % mod * x % mod) % mod;
            n = n / 2;
        }
        return result;
    }

    public static int modularExponentiation(int x, int n, int M) {
        int result = 1;
        while (n > 0) {
            if (n % 2 == 1)
                result = (result * x) % M;
            x = (x * x) % M;
            n = n / 2;
        }
        return result;
    }

    public static long modularExponentiation(long x, long n, long M) {
        long result = 1;
        while (n > 0) {
            if (n % 2 == 1)
                result = (result * x) % M;
            x = (x * x) % M;
            n = n / 2;
        }
        return result;
    }

    public static int modInverse(int A, int M) {
        return modularExponentiation(A, M - 2, M);
    }

    public static long sie(long A, long M) {
        return modularExponentiation(A, M - 2, M);
    }

    public static boolean checkYear(int year) {
        if (year % 400 == 0)
            return true;

        if (year % 100 == 0)
            return false;

        if (year % 4 == 0)
            return true;
        return false;
    }

    public static boolean isPrime(int n) {

        if (n <= 1)
            return false;
        if (n <= 3)
            return true;

        if (n % 2 == 0 || n % 3 == 0)
            return false;

        for (int i = 5; i * i <= n; i = i + 6) {
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
        }

        return true;
    }

    static class pair implements Comparable<pair>

    {
        Integer x, y;

        pair(int x, int y) {
            this.x = x;
            this.y = y;
        }

        public int compareTo(pair o) {
            int result = x.compareTo(o.x);
            if (result == 0)
                result = y.compareTo(o.y);

            return result;
        }

        public String toString() {
            return x + " " + y;
        }

        public boolean equals(Object o) {
            if (o instanceof pair) {
                pair p = (pair) o;
                return p.x == x && p.y == y;
            }
            return false;
        }

        public int hashCode() {
            return new Long(x).hashCode() * 31 + new Long(y).hashCode();
        }

    }

    static class triplet implements Comparable<triplet> {
        Integer x, y, z;

        triplet(int x, int y, int z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }

        public int compareTo(triplet o) {
            int result = x.compareTo(o.x);
            if (result == 0)
                result = y.compareTo(o.y);
            if (result == 0)
                result = z.compareTo(o.z);

            return result;
        }

        public boolean equlas(Object o) {
            if (o instanceof triplet) {
                triplet p = (triplet) o;
                return x == p.x && y == p.y && z == p.z;
            }
            return false;
        }

        public String toString() {
            return x + " " + y + " " + z;
        }

        public int hashCode() {
            return new Long(x).hashCode() * 31 + new Long(y).hashCode() + new Long(z).hashCode();
        }
    }

    
    
    /*
     * static class node implements Comparable<node>
     * 
     * { Integer x, y, z; node(int x,int y, int z) { this.x=x; this.y=y; this.z=z; }
     * 
     * public int compareTo(pair o) { int result = x.compareTo(o.x); if(result==0)
     * result = y.compareTo(o.y); if(result==0) result = z.compareTo(z); return
     * result; }
     * 
     * @Override public int compareTo(node o) { // TODO Auto-generated method stub
     * return 0; } }
     */
}

