Problem:
Score : 700 points

Problem Statement

Snuke loves constructing integer sequences.

There are N piles of stones, numbered 1 through N.
The pile numbered i consists of a_i stones.

Snuke will construct an integer sequence s of length Σa_i, as follows:

Among the piles with the largest number of stones remaining, let x be the index of the pile with the smallest index. Append x to the end of s.

Select a pile with one or more stones remaining, and remove a stone from that pile.

If there is a pile with one or more stones remaining, go back to step 1. Otherwise, terminate the process.

We are interested in the lexicographically smallest sequence that can be constructed. For each of the integers 1,2,3,...,N, how many times does it occur in the lexicographically smallest sequence?

Constraints

1 ≤ N ≤ 10^{5}

1 ≤ a_i ≤ 10^{9}

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 ... a_{N}

Output

Print N lines. The i-th line should contain the number of the occurrences of the integer i in the lexicographically smallest sequence that can be constructed.

Sample Input 1

2
1 2

Sample Output 1

2
1

The lexicographically smallest sequence is constructed as follows:

Since the pile with the largest number of stones remaining is pile 2, append 2 to the end of s. Then, remove a stone from pile 2.

Since the piles with the largest number of stones remaining are pile 1 and 2, append 1 to the end of s (we take the smallest index). Then, remove a stone from pile 2.

Since the pile with the largest number of stones remaining is pile 1, append 1 to the end of s. Then, remove a stone from pile 1.

The resulting sequence is (2,1,1). In this sequence, 1 occurs twice, and 2 occurs once.

Sample Input 2

10
1 2 1 3 2 4 2 5 8 1

Sample Output 2

10
7
0
4
0
3
0
2
3
0

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

/*
cat <<EOF >mistaken-paste
*/

#pragma GCC diagnostic ignored "-Wincompatible-pointer-types"

#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>

#define BIG 2000000007
#define VERYBIG 200000000000007LL

#define MOD 1000000007
typedef uint64_t ull;
typedef  int64_t sll;

#define N_MAX 200000
#define M_MAX 100000

#ifdef __cplusplus
#include <queue>
#include <stack>

using namespace std; // I'm NOT gonna use C++ without compro. shit

typedef priority_queue<ull, vector<ull>, greater<ull> > upque123;
typedef priority_queue<ull, vector<ull> > upque321;
typedef priority_queue<sll, vector<sll>, greater<sll> > spque123;
typedef priority_queue<sll, vector<sll> > spque321;

#endif

typedef struct {
	int32_t a;
	int32_t b;
} hw;

typedef struct {
	sll a;
	sll b;
} hwll;

typedef struct {
	hwll a;
	hwll b;
} linell;


typedef struct {
	ull s;
	ull t;
	int32_t c;
} struct_a;

typedef struct {
	int32_t from;
	int32_t to;
	sll cost;
} struct_b;



const hw vector8[8] = {
	{-1, -1},
	{-1,  0},
	{-1, +1},
	{ 0, -1},
	{ 0, +1},
	{+1, -1},
	{+1,  0},
	{+1, +1}
};

ull n, m;
ull h, w;
ull k;
ull vua, vub, vuc, vud, vue, vuf;
sll vsa, vsb, vsc, vsd, vse, vsf;
long double vra, vrb, vrc;
double vda, vdb, vdc;
size_t slen;
size_t tlen;
char ch, dh;
ull a[N_MAX];
// ull a[M_MAX];
// sll a[N_MAX];
// ull a[N_MAX][N_MAX];
// ull wall[N_MAX][N_MAX];
// double wall[N_MAX][N_MAX];
ull b[N_MAX];
// ull b[M_MAX];
// sll b[N_MAX];
// ull b[N_MAX][N_MAX];
// sll b[N_MAX][N_MAX];
ull c[N_MAX];
// ull c[M_MAX];
// sll c[N_MAX];
// char s[N_MAX + 1];
// char t[N_MAX + 1];
// char s[N_MAX][M_MAX + 1];
// ull alphabets[26];

// ull dp[N_MAX];
// sll dp[N_MAX];
// bool dp[N_MAX];
// int32_t dp[N_MAX];
// ull dp[N_MAX + 1][N_MAX + 1];
// ull dp[N_MAX * N_MAX];
// double dp[N_MAX];
// double dp[N_MAX][70][40][30];
// ull dq[N_MAX];
// ull dq[N_MAX + 1][N_MAX + 1];
// sll dq[N_MAX];
// bool dq[N_MAX];
// double dq[N_MAX];
// hwll dp[N_MAX + 1][N_MAX + 1];
// struct_a dp[N_MAX + 1][N_MAX + 1];

// sll imos[N_MAX + 5];


// hw arr[N_MAX];
hwll arr[N_MAX * 2];
// hw brr[M_MAX];
hwll brr[N_MAX];
// linell arr[N_MAX][N_MAX];

// ull bitdp[1 << 8];

// ull digitdp[1001][   3][    2];
//           pos  less  carry
// ull digitdp[1001][    2];
//           pos  carry


// struct_a arr[N_MAX * 2];
// struct_b brr[N_MAX * 2];

void swap_adj (ull *a, ull *b) {
	if (*a != *b) {
		ull tmp = *b;
		*b = *a;
		*a = tmp;
	}
	return;
}

ull divide (ull a, ull b) {
	ull x = MOD - 2;
	ull ans = 1;
	while (x) {
		if (x & 1) ans = (ans * b) % MOD;
		b = (b * b) % MOD;
		x /= 2;
	}
	return (a * ans) % MOD;
}

int32_t digits (ull x) {
	int32_t i = 1;
	while (x >= 10) {
		x /= 10;
		i++;
	}
	return i;
}

ull umin (ull x, ull y) {
	return (x < y) ? x : y;
}

ull umax (ull x, ull y) {
	return (x > y) ? x : y;
}

sll smin (sll x, sll y) {
	return (x < y) ? x : y;
}

sll smax (sll x, sll y) {
	return (x > y) ? x : y;
}

ull gcd (ull x, ull y) {
	if (x < y) {
		return gcd(y, x);
	} else if (y == 0) {
		return x;
	} else {
		return gcd(y, x % y);
	}
}

ull bitpow (ull a, ull x, ull modulo) {
	ull result = 1;
	while (x) {
		if (x & 1) {
			result *= a;
			result %= modulo;
		}
		x /= 2;
		a = (a * a) % modulo;
	}
	return result;
}

int32_t targetdig (ull x, int32_t index /* 1-indexed */) {
	// static...?
	int32_t posmax = digits(x);
	if (posmax < index) return -1;
	while (posmax > index) {
		posmax--;
		x /= 10;
	}
	return x % 10;
}

int32_t charcomp (const char left, const char right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int32_t pcharcomp (const void *left, const void *right) {
	char lval = *(char*)left;
	char rval = *(char*)right;
	return charcomp(lval, rval);
}

int32_t intcomp (const int32_t left, const int32_t right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int32_t pintcomp (const void *left, const void *right) {
	int lval = *(int*)left;
	int rval = *(int*)right;
	return intcomp(lval, rval);
}

int32_t ullcomp (const ull left, const ull right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int32_t pullcomp (const void *left, const void *right) {
	ull lval = *(ull*)left;
	ull rval = *(ull*)right;
	return ullcomp(lval, rval);
}

int32_t sllcomp (const sll left, const sll right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int32_t psllcomp (const void *left, const void *right) {
	sll lval = *(sll*)left, rval = *(sll*)right;
	return ullcomp(lval, rval);
}

int32_t hwllfraccomp (const hwll left, const hwll right) {
	return ullcomp(left.a * right.b, left.b * right.a);
}

int32_t phwAcomp (const hw *left, const hw *right) {
	return intcomp(left->a, right->a);
}

int32_t phwBcomp (const hw *left, const hw *right) {
	return intcomp(left->b, right->b);
}

int32_t phwABcomp (const hw *left, const hw *right) {
	int32_t x = phwAcomp(left, right);
	if (x) return x;
	return phwBcomp(left, right);
}

int32_t phwllAcomp (const hwll *left, const hwll *right) {
	return sllcomp(left->a, right->a);
}

int32_t phwllBcomp (const hwll *left, const hwll *right) {
	return sllcomp(left->b, right->b);
}

int32_t phwllABcomp (const hwll *left, const hwll *right) {
	int32_t x = phwllAcomp(left, right);
	if (x) return x;
	return phwllBcomp(left, right);
}

int32_t phwllrAcBcomp (const hwll *left, const hwll *right) {
	int32_t x = -phwllAcomp(left, right);
	if (x) return x;
	return phwllBcomp(left, right);
}

int32_t phwllBAcomp (const hwll *left, const hwll *right) {
	int32_t x = phwllBcomp(left, right);
	if (x) return x;
	return phwllAcomp(left, right);
}

int32_t pstrAcomp (const struct_a *left, const struct_a *right) {
	int32_t x;
	if (x = ullcomp(left->t, right->t)) return x;
	if (x = ullcomp(left->s, right->s)) return x;
	if (x = intcomp(left->c, right->c)) return x;
	return 0;
}

int32_t bitlet (char c) {
	return (1 << (c - 'a'));
}

ull ullabs (ull a, ull b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

sll sllabs (sll a, sll b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

sll nibutanlobo (bool (*func)(sll arg), sll ok, sll ng) {
	while (sllabs(ok, ng) > 1) {
		sll med = (ok + ng) / 2;
		if (func(med)) {
			ok = med;
		} else {
			ng = med;
		}

		// printf("debug: [%lld %lld)\n", ok, ng);
	}

	if (!func(ok)) return ok * 2 - ng;
	return ok;
}

bool nextroute (int32_t arr[], int32_t n) {
	int32_t i = n - 1;
	int32_t j, x;

	while (i > 0 && arr[i - 1] > arr[i]) i--;
	if (i == 0) return false;

	x = n;
	for (j = i; j < n; j++) {
		if (arr[j] < arr[i - 1]) continue;
		if (x == n || arr[x] > arr[j]) x = j;
	}
	arr[i - 1] ^= arr[x];
	arr[x] ^= arr[i - 1];
	arr[i - 1] ^= arr[x];

	qsort(&arr[i], n - i, sizeof(int32_t), pintcomp);
	return true;
}

void printUquotient (ull left, ull right) {
	const int32_t digits = 20;

	printf("%llu.", left / right);
	left %= right;
	for (int32_t i = 0; i < digits; i++) {
		left *= 10;
		printf("%1d", left / right);
		left %= right;
	}
	puts("");

	return;
}

void printSquotient (sll left, sll right) {
	if (left * right < 0) putchar('-');
	printUquotient(sllabs(left, 0), sllabs(right, 0));

	return;
}

int bitcount (ull n) {
	int result = 0;
	while (n) {
		if (n & 1) result++;
		n /= 2;
	}
	return result;
}

#ifdef __cplusplus

typedef struct {
	int32_t to;
	sll cost;
} edge;
typedef pair<sll, int32_t> P;

std::vector<edge> g[N_MAX];
void dijk_init (ull n, struct_b arr[]) {
	edge x;
	for (int32_t i = 0; i < n; i++) {
		x.to = arr[i].to;
		x.cost = arr[i].cost;
		g[arr[i].from].push_back(x);
	}
}

void dijkstra (int s, sll distance[]) {
	priority_queue<P, std::vector<P>, greater<P> > que; // (最短距離, 頂点番号)
	for (int32_t i = 0; i < n; i++) {
		distance[i] = BIG;
	}
	distance[s] = 0;
	que.push(P(0, s));

	while (!que.empty()) {
		P p = que.top();
		que.pop();

		sll v = p.second;
		if (distance[v] < p.first) continue;

		int32_t maxsize = g[v].size();
		for (int32_t i = 0; i < maxsize; i++) {
			edge e = g[v][i];
			if (distance[e.to] > distance[v] + e.cost) {
				distance[e.to] = distance[v] + e.cost;
				que.push(P(distance[e.to], e.to));
			}
		}
	}

	return;
}

#endif


double distance (sll x1, sll y1, sll x2, sll y2) {
	double xdist2, ydist2, origindist, dist;

	xdist2 = (x1 - x2) * (x1 - x2);
	ydist2 = (y1 - y2) * (y1 - y2);
	return sqrt(xdist2 + ydist2);
}

ull solve () {
	sll i, j, ki, l;
	ull result = 0;
	// sll result = 0;
	// double result = 0;
	ull sum = 0;
	// sll sum = 0;
	ull item;
	ull *dpcell;
	// qsortの際には"p"ullcompを使う

	for (i = 0; i < n; i++) {
		arr[i].a = a[i];
		arr[i].b = i;
	}
	qsort(arr, n, sizeof(hwll), phwllrAcBcomp);

	i = 0;
	ki = 0;
	ull smallest = arr[0].b;
	while (i < n) {
		j = i;
		while (j < n - 1) {
			if (arr[i].a != arr[j + 1].a) break;
			j++;
		}
		if (arr[i].b < smallest) smallest = arr[i].b;
		b[smallest] += (arr[i].a - ((j < n - 1) ? arr[j + 1].a : 0)) * (j + 1);

		i = j + 1;
	}
	for (i = 0; i < n; i++) {
		printf("%llu\n", b[i]);
	}

	// printf("%llu\n", result);
	// printf("%.12lf\n", result);
	// puts(s);

	return 0;

	success:
	// puts("YES");
	// puts("Yes");
	// printf("%llu\n", result);
	// puts("Alice");
	return 0;

	fail:
	// puts("NO");
	// puts("No");
	// puts("0");
	puts("-1");
	// puts("-1 -1 -1");
	// puts("Brown");
	return 1;
}

int32_t main (void) {
	int32_t i, j;
	int32_t x, y;

	// scanf("%lf", &vda);
	// scanf("%lld%lld%lld%lld", &vsa, &vsb, &vsc, &vsd);
	// scanf("%llu%llu", &h, &w);
	scanf("%llu", &n, &m);
	// scanf("%llu", &k, &n);
	// scanf("%llu%llu", &vua, &vub, &vuc, &vud, &vue);
	// scanf("%llu%llu%llu", &vsa, &vsb, &vsc);
	// scanf("%s", s);
	// scanf("%s", t);
	// scanf("%lld%lld", &vsa, &vsb);
	for (i = 0; i < n; i++) {
		scanf("%llu", &a[i]);
		// a[i]--;
	}

	// for (i = 0; i < k; i++) {
	// 	scanf("%d", &dp[i]);
	// 	dp[i]--;
	// }
	// for (i = 0; i < n; i++) {
	// 	scanf("%s", s[i]);
	// }
	// for (i = 0; i < h; i++) {
	// 	scanf("%llu", &a[i]);
	// }
	// for (i = 0; i < w; i++) {
	// 	scanf("%llu", &b[i]);
	// }
	// for (i = 0; i < n; i++) {
	// 	scanf("%llu%llu", &a[i], &b[i]);
	// }
	// for (i = 0; i < h; i++) {
	// 	for (j = 0; j < w; j++) {
	// 		scanf("%llu", &a[i][j]);
	// 	}
	// }

	solve();

	// for (i = 0; i < n; i++) {
	// 	// scanf("%llu%llu", &vua, &vub);
	// 	scanf("%s%s", s, t);
	// 	// scanf("%f%f%f", &vda, &vdb, &vdc);
	// 	// scanf("%s", s);
	// 	solve();
	// }

	// while (scanf("%llu%llu", &n, &k), n + k) {
	// 	for (i = 0; i < n; i++) {
	// 		scanf("%llu", &a[i]);
	// 	}
	// 	solve();
	// }

	return 0;
}